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NEW  ELEMENTARY 
ARITHMETIC 

THE  NORMAL  COURSE  IN  NUMBEI 


INDIANA-  EDITION 


SILVER,  BURDETT  AND  COMPAHY    f 


"^^^  UNIVERSITY   OF   CALIFORNIA 

DEP  ^ 


No, 


cT 


Digitized  by  the  Internet  Archive 

in  2008  with  funding  from 

IVIicrosoft  Corporation 


http://www.archive.org/details/cookarithmetic'OOcookrich 


_  ..•;  •: :  v  ,     •... 

THE    NEW      *****'-*^*' 
ELEMENTARY  ARITHMETIC 

BY 
JOHN  W.   COOK 

PRESIDENT   OF   ILLINOIS  STATE   NORMAL   UNIVERSITY 
AND 

MISS  N.   CEOPSEY 

ASSISTANT   SUPERINTENDENT   OF   CITY   SCHOOLS,    INDIANAPOLIS,   INDIANA 


REVISED   BY 
ROBERT  J.  ALEY 

PROFESSOR   OF   MATHEMATICS,    INDIANA   UNIVERSITY 
AND 

OSCAR  L.   KELSO 

PROFESSOR  OF  MATHEMATICS,   INDIANA  STATE  NORMAL  SCHOOL 


SILVER,  BURDETT  AND  COMPANY 
NEW  YORK  BOSTON  CHICAGO 


CopTRiGUT  im:\,  1895,  i^\r.),  iixxi. 

By  silver,  BtJRDETT  AND   COMPANY 

EDUCATION  DEPi. 


PEEFACE  TO  THE  KEVISED  EDITION 

The  present  edition  of  "  The  ]^ew  Elementary  Arith- 
metic" will  be  found  to  differ  from  the  earlier  edition 
])rincipally  in  an  increase  in  the  amount  of  drill  work 
given  upon  the  fundamental  operations.  This  change,  it 
is  believed,  recognizes  a  tendency  of  present-day  arith- 
metic work  which  has  the  approval  of  the  best  authorities. 

In  a  few  other  respects  also  the  book  has  been  changed, 
notably  in  the  direction  of  simplification  and  the  bringing 
of  the  book  into  harmony  Avith  the  advance  which  has 
been  made  in  the  teaching  of  arithmetic  since  the  first 
edition  appeared. 

In  making  these  changes,  the  arrangement  of  the  mat- 
ter has  been  altered,  a  large  number  of  new  exercises  have 
been  added,  and  the  problems  in  many  cases  have  been 
rewritten  or  replaced. 

It  is  hoped  that  the  present  book  will  be  found  thor- 
oughly abreast  of  the  best  practice  in  the  teaching  of 
arithmetic,  and  that  in  its  new  form  the  work  will  con- 
tinue to  enjoy  the  confidence  and  appreciation  which  have 
been  so  kindly  extended  to  it  up  to  the  present  time. 


54IS33 


PREFACE  TO  THE  FIRST  EDITION. 


IT  has  seemed  to  the  authors  of  the  Normal  Course 
IN  Number  that  there  is  room  for  another  series  of 
Arithmetics,  notwithstanding  the  fact  that  there  are  many 
admirable  books  on  the  subject  already  in  the  field. 

The  Elementary  Arithmetic  is  the  result  of  the  ex- 
perience of  a  supervisor  of  primary  schools  in  a  leading 
American  city.  Finding  it  quite  impossible  to  secure 
satisfactory  results  by  the  use  of  such  elementary  arith- 
metics as  were  available,  she  began  the  experiment  of 
supplying  supplementary  material.  An  effort  was  made 
to  prepare  problems  that  should  be  in  the  highest  degree 
practical,  that  should  develop  the  subject  systematically, 
and  that  should  appeal  constantly  to  the  child's  ability  to 
think.  The  accumulations  of  several  years  have  been  care- 
fully re-examined,  re-arranged,  and  supplemented,  and  are 
now  presented  to  the  public  for  its  candid  consideration. 

Not  the  least  valuable  feature  of  this  book  is  the  care- 
ful gradation  of  the  examples,  securing  thereby  a  natural 
and  logical  development  of  number  work.  No  space  is 
occupied  with  the  presentation  of  theory,  —  that  side  of 
the  subject  being  left  to  the  succeeding  book.  The  first 
thoughts  SLve  ivhat  and  hoWj — these  so  presented  that  the 
processes  shall  be  easily  comprehended  and  mastered. 
Subsequently,  the  tchf/  may  be  intelligently  considered  and 
readily  understood. 


INTRODUCTION. 


It  has  been  said  that  the  "  new  education  "  proceeds  to 
give  the  child  an  experience,  instead  of  presupposing  one 
for  him.  Pupils  become  practical,  not  by  learning  forms 
of  reasoning,  but  by  exercising  the  reason  upon  their  own 
plane  of  comprehension.  In  such  a  spirit  this  Elemen- 
tary Arithmetic  has  been  prepared.  It  presents  three- 
years'  work,  based  upon  carefully  graded  exercises  which 
may  be  used  as  a  means  of  training  pupils  to  think,  and 
of  teaching  at  the  same  time  the  practical  application  of 
numbers  to  ordinary  business  transactions. 

It  is  very  important  that  children  should  master  the 
fundamental  processes  so  thoroughly  that  they  come  to 
serve  thought  without  loss  of  time  or  energy.  The 
patient  following  of  these  graded  exercises  and  drills 
should  secure  this  result.  In  general,  division  and  multi- 
plication, as  converse  processes,  are  followed  by  addition 
and  subtraction  on  the  same  general  plan.  As  the  work 
becomes  more  complex,  it  is  diiRcult  to  make  this  alterna- 
tion with  perfect  regularity  without  detriment  to  the 
efficiency  of  the  work.  Stress  must  be  laid  upon  such  a 
complex  subject  as  long  division,  a  very  difficult  subject 
for  children,  which  requires  an  amount  of  practice  that, 
at  first  view,  might  seem  out  of  proportion  to  the  practice 
given  in  other  subjects. 

The  primary  facts  of  addition  and  subtraction  are  pre- 
sented in  the  first  twenty  pages.  Neither  accuracy  nor 
rapidity  in  calculation  can  be  secured  until  these  combina- 


vi  INTRODUCTION. 

tions  can  be  given  with  readiness.  Those  facts  are  used 
again  in  the  tables  of  ''endings,"  for  ai)|)lication  to  num- 
bers above  twenty.  These  tables  have  a  practical  value  and 
should  be  as  thoroughly  applied  as  the  multiplication  and 
division  tables.  These  tables  in  subtraction  give  an  oppor- 
tunity for  reviewing  the  primary  facts,  and  for  using  this 
knowledge  with  numbers  above  tvoenty^hvX  they  have  no 
such  direct  application  as  the  tables  in  addition.  Any 
reasonable  system  of  teaching  addition  can  be  used  with 
the  graded  examples  of  the  Elementary  Arithmetic. 

The  first  and  hardest  step  in  solving  an  arithmetical 
question  is  to  determine  the  processes  required ;  the  sec- 
ond, to  state  the  different  steps  of  the  solution  in  proper 
arithmetical  form.  Children  can  give  results  long  before 
they  are  conscious  of  the  process  by  which  the  results  are 
obtained.  The  statement  of  the  process  by  means  of 
arithmetical  signs  and  figures  is  a  new  language  to  the 
pupil;  it  is  not  surprising  that  the  mastery  of  tliis  lan- 
guage takes  time  and  skillful  teaching.  The  statement 
of  the  result,  in  a  concrete  problem,  is  probably  all  that 
should  be  required  in  the  second  school  year.  Tt  may  be 
desirable  to  introduce  a  simple  statement  of  the  process 
early  in  the  third  year.  Such  a  statement  can  be  added 
to  the  sentence  giving  the  result,  as  on-  page  16,  example 
1 :  4  cents  x  3  =  12  cents.  No  formula  should  be  taught 
with  the  thought  that  it  will  do  the  thinking  for  the 
pupil.  Let  the  problem  be  pictured,  and  this  picturing 
followed  by  the  expression  in  figures,  before  any  formal 
expression  in  Avords  is  attempted.  The  object  of  pictur- 
ing problems  is  not  to  teach  children  to  make  pictures 
(though  all  this  work  should  be  done  with  reasonable 
care),  but  to  give  a  method  of  representation  by  Avhich 
they  can  make  their  thoughts  clear  to  themselves.     It  is 


INTRODUCTION.  vii 

a  means,  not  an  end,  and  should  be  so  regarded.  When 
problems  can  be  stated  clearly  and  solved  correctly  there 
is  no  further  necessity  for  picture  representation,  except 
as  a  means  of  testing  the  pupiPs  comprehension  of  spoken 
or  written  forms.  Let  not  objective  work  be  undervalued, 
however.  It  is  a  very  necessary  means,  which,  rightly 
used,  will  secure  accurate  knowledge  and  a  correct  use  of 
terms,  thus  saving  much  time  and  confusion  later  on. 
Pupils  should  learn  early  to  show  objectively  the  differ- 
ence between  six  and  one-sixth  of  six,  between  one-sixth 
of  six  and  one-sixth  of  07ie,  etc. 

Problems  which  may  be  worked  out  orally  in  the  reci- 
tation will  often  be  found  too  diificult  for  a  written  test. 
"Miscellaneous  problems"  should  be  used  with  discrimi- 
nation, the  teacher  selecting  such  as  seem  suited  to  the 
capacity  of  the  class. 

All  measures  introduced  should  be  learned  by  actual 
use.  The  standards  in  common  use,  such  as  the  yard, 
foot,  ounce,  pound,  quart,  etc.,  can  be  obtained  easily,  and 
should  form  a  part  of  the  regular  school  supplies.  Exer- 
cises in  estimating  volume  and  extension  train  the  judg- 
ment while  giving  practical  results  in  knowledge,  and 
there  is  no  time  in  the  course  when  pupils  can  better 
afford  to  do  this  work  than  during  the  first  years  of  the 
elementary  school  course. 

Eules  may  be  made  by  the  pupils  after  the  process  is 
learned  from  which  the  rule  is  derived. 

This  book  has  grown  from  experience,  and  is  offered  to 
fellow-teachers  as  a  systematic  work-book. 


CONTENTS. 

PAGE 

Chapter  I 1_24 

Numbers  Through  Twelve 1 

The  One-Inch  Square  and  the  Inch 7 

Pints  and  Quarts 8 

Numbers  Through  Seventeen 9 

Numbers  from  Ten  to  Twenty,  as  Tens  and  Ones       .        .        .18 

Writing  Numbers  to  Ten 19 

The  Numbers  Eighteen,  Nineteen  and  Twenty  ....     19 
Comparison  of  Halves  and  Fourths 31 

Chapter  II         .        .        . 25-41 

Numbers  from  Twenty  to  One  Hundred,  as  Tens  and  Ones        .     25 

Writing  Numbers  from  Ten  to  Thirty 27 

Addition  and  Subtraction .28 

Quarts  and  Gallons 31 

Multiplication  and  Division         . 32 

Chapter  III 42-61 

Reading  and  Writing  Numbers  :  Hundreds        .        .        .        .42 

Addition 45 

Subtraction .        .        .46 

Inch,  Foot  and  Yard 49 

Measuring  Time  .         . 53 

Multiplication  and  Division 55 

Chapter  IV 62-116 

Reading  and  Writing  Numbers  :  Thousands       .        .        .        .62 

Roman  Notation 64 

Multiplication 65 

Division 67 

Multiplying  and  Dividing  by  3 69 

Multiplying  and  Dividing  by  4,  5  and  6 70 

United  States  Money 72 

Addition  and  Subtraction  by   Endings  :   1  +  8,  1  +  9,  2  +  5, 
2  +  6,  3  -f  7 74 


X  CONTENTS. 

Dry  Measures 79 

Addition  and  Subtraction  by  Endings  :  2  +  8,  2  +  9  .        .83 

Ounces  and  Pounds 85 

Addition   and  Subtraction  by  Endings :  3  +  5,  0+6,  3  +  7, 

3  +  8,  3  +  9 88 

Comparison  of  Halves,  Fourths  and  Eighths      .        .        .        .96 

Multiplication  and  Division 100 

Multiplying  and  Dividing  by  7  and  8 103 

Addition  and  Subtraction  by  Endings  :  4  +  4.  4  +  5,  4  +  0        .  109 
Multiplication  and  Division Ill 

Chapter  V 117-137 

Reading  and  Writing  Numbers 117 

Multiplying  and  Dividing  by  9,  10,  11  and  12     .  .        .119 

Addition  and  Subtraction  by  Endings  :  4  +  7,  4  +  8  .        .        .  124 

Multiplication 128 

United  States  Money 129 

Addition  and  Subtraction  by  Endings  :  4  +  9     .        .        .        .  131 
Halves,  Thirds  and  Sixths 135 

Chapter  VI 138-202 

Multiplication  and  Division 138 

Addition  and  Subtraction  by  Endings  :  5  +  5,  5  +  6,  5  +  7,  5  +  8  .  142 

Multiplication  and  Division .  152 

Addition  and  Subtraction  by  Endings  :  5  +  9    .        .        ,        .  154 

Multiplication  and  Division 160 

Comparison  of  Halves,  Thirds,  Fourths  and  Sixths    .        .        .  164 

Division 167 

Addition  and  Subtraction  by  Endings  :  6  +  6.  64-7.  6  +  8,  6  +  9  .  168 

Division 172 

United  States  Money 174 

Square  Measure    .        .        .        ,        , 176 

Addition  and  Snbtraction  by  Endings  :  7+7,   7  +  8,   7+9, 

8  +  8,  8  +  9 179 

Cubic  Measure 187 

Multiplication  and  Division 190 

Addition  and  Subtraction  by  Endings  :  9  +  9    .  .        .  190 

Division 195 

Addition  and  Subtraction    .        .......  195 

Division 200 


CONTENTS.  xi 

I'AGE 

Chapter  VII 203-241 

Fractions ,        ^  203 

Like  and  Unlike  Numbers 204 

Reduction 207 

Addition  of  Fractions 212 

Subtraction  of  Fractions 215 

Division  of  Fractions 219 

Multiplication  of  Fractions 226 

Chapter  VIII 242-261 

Decimal  Fractions 242 

Writing  and  Reading  Decimals 246 

Reduction 247 

Addition  of  Decimals 249 

Subtraction  of  Decimals 250 

Division  of  Decimals 251 

Multiplication  of  Decimals 256 

Chapter  IX 262-276 

Compound  Numbers     .         .        . 262 

Dry  Measure 262 

Liquid  Measure 265 

Avoirdupois  Weight 265 

Measures  of  Length 267 

Square  Measure 268 

Cubic  Measure      ....  270 

Time  Measure      ....  273 


THE  NEW 
ELEMENTARY  ARITHMETIC. 

CHAPTER  I. 

I2345bngq 

1.  Write  the  names  of  the  numbers  from  one  to  ten. 
Write  the  figures  which  stand  for  these  numbers. 
Count  one  hundred  by  ones;  by  tens. 

NUMBERS  THROUGH  TWELVE. 

[A  review  of  work  learned  in  the  second  school  year.] 

2.  Count  by  ones  through  twelve;  count  by  twos;  by 
threes;  by  fours. 

Begin  with  twelve  and  name  the  numbers  in  their  order 
to  one. 

Name  two  numbers  which  together  make  four;  two 
numbers  which  make  six. 


NUMBERS   THROUGH   TWELVE. 


Addition  and  Subtraction 

u 

3,           Sums 

of  any  two  numbers  through  eight 

112        1 

2 

12     3        1 

2 

3      12     3 

4 

2       3     24 

3 

5     4     3        6 

5 

4      7     6     5 

4 

3      4     4       5 

5 

6     6     6        7 

7 

7      8     8     8 

8 

1  and  2  are  — 

5  less  3   is   — 

7  less  5  is 



3  less  2   is  — 

1  and  5  are  — 

4  and  3  are 

— 

1  and  3  are  — 

6  less  5   is  — 

7  less  3   is 

— 

4  less  3  is  — 

4  and  2  are  — 

7  less  4  is 

— 

2  and  2  are  — 

6  less  2   is   — 

6  and  2  are 

— 

4  less  2  is  — 

3  and  3  are  — 

8  less  2  is 

— 

1  and  4  are  — 

6  less  3   is   — 

8  less  6  is 

— 

5  less  4  is   — 

5  and  2  are  — 

5  and  3  are 

— 

2  and  3  are  — 

7  less  2   is   — 

8  less  3  is 

— 

4.  What  two  equ^l  numbers  make  four? 

Separate  four  into  two  equal  parts.  Take  away  one  of 
of  the  parts;  what  is  left? 

Separate  eight  into  two  equal  parts.  Take  away  one  of 
the  parts;  what  is  left? 

Separate  eight  into  two  unequal  parts.  Take  away  one 
of  the  parts;  what  number  is  left? 

5,  Sums  of  any  two  numbers  through  twelve. 

1234  12345  12345 

^    1    ^    ^         ^8_7_6     5         10_9876 
9     9     9     9         10  10  10  10  10         11  11  11  11  11 


ADDITION  AND  SUBTRACTION.  3 

12       3       4       5       6 

11  10       9     J       7       6 

12  12     12     12     12     12 

7  and  2  are  —  7  and  3  are  — 
9  less  7  is  —  10  less  3  is  — 
6  and  3  are  —  10  less  7  is  — 
9  less  3  is  —  6  and  4  are  — 

5  and  4  are  —  10  less  4  is  — 
9  less  4  is  —  10  less  6  is  — 
9  less  5  is  — ^  9  and  2  are  — 

8  and  2  are  —  11  less  2  is  — 

10  less  2  is  —  11  less  9  is  — 

8  and  3  are  —  9  and  3  are  — 

11  less  3  is  —  12  less  3  is  — 
11  less  8  is  —  8  and  4  are  — 

6  and  5  are  —  12  less  4  is  — 
11  less  5  is  —  12  less  8  is  — 
11  less  6  is  —  7  and  5  are  — 

7  and  4  are  —  12  less  5  is  — 
11  less  4  is  —  12  less  7  is  — 
11  less  7  is  —  12  less  6  is  — 

6.  Find  the  sunis^  giving  results  only: 

24212324  124375513 
4^563574865423496 

Note  to  Teachers. — If  the  children  are  not  very  faniihar  witli 
these  fundamental  facts,  sufficient  time  must  be  given  to  secure  a 
thorough  mastery  of  them.  If  necessary,  the  work  must  be  given 
with  the  objects.  As  soon  as  possible;  however,  children  should 
becoriie  independent  of  the  use  of  objects. 


NUMBERS   THROUGH   TWELVE. 


2    5 

3 

8 

4 

6 

7 

9 

6    2 

5 

3 

5 

3 

3 

4 

9 

8    2 

7 

2 

6 

3 

3 

1 

4    9 

6 

7 

4 

5 

8 

7 

2 

8 

6 

3 

4 

3 

4 

7 

5  10 

6 

8 

9 

6 

5 

7 

3 

3 

9 

8 

4 

5 

3 

7    2 

6 

2 

3 

5 

7 

4 

Supply  the  numbers  omitted: 
6       6234      6    2517      3      3654 

10     11897129116121110989 

4475987893 
12    IT     10     12     11     12     IT    lO     11     12 

Subtract  at  sight,  giving  results  only : 

8675689     10    87     11     12     10    876 
5432465      672      6      7      8522 


11    9     10    11     12    9     10    7     10    12 
5376523184 


11     9    8     12     12     11     12     12 

_484_7_8_8_9j; 

7.  1.  Henry  bought  a  book  for  8  cents  and  a  pencil  for 
4  cents;  he  paid  —  cents  for  both. 


MULTIPLICATION  AND  DIVISION.  5 

2.  There  were  4  boys  and  6  girls  in  a  class;  together 
there  were  —  children. 

3.  Helen  had  11  roses  and  gave  4  of   them  to  May; 
Helen  then  had  —  roses. 

4.  James  earned  7  cents  and  George  earned  5  cents; 
together  they  earned  —  cents. 


5.  Make  problems  for: 

6  and  3  are  9. 
10  less  6  is  4. 


9  and  3  are  12. 
11  less  5  is     6. 


Note. — The  children  should  group  objects  and  make  the 
problems  with  the  objects  before  them.  This  work  is  for  the 
recitation,  not  the  study  period. 


Multiplication  and  Division. 


8.      (1) 

2  twos  are  — 

3  twos  are  — 

4  twos  are  — 

5  twos  are  — 


(2) 

6  twos  are  — 

2  threes  are  — 

3  threes  are  — 

4  threes  are  — 


(3) 

2  fours  are  — 

3  fours  are  — 
2  fives  are  — 
2  sixes  are  — 


(4)  (6)  (6) 

6  is  —  twos.  12  is  —  threes.         8  is  —  fours. 

8  is  —  twos.  12  is  —  fours.  6  is  —  threes. 

9  is  —  threes.  12  is  —  sixes.  10  is  —  fives. 


(7) 

One-half  of  4  is  — 
One-half  of  6  is  — 
One-half  of  8  is  — 


(8) 

One-half  of  10  is  - 
One-half  of  12  is  - 
One-third  of  6  is  - 


6  NUMBERS  THROUGH   TWELVE. 

(0)  (lo) 

One-third  of      9  is  —  J  of    9  is  — 

One-third  of    12  is  —  i  of  12  is  — 

One-fourth  of    8  is  —  i  of    8  is  — 

One-fourth  of  12  is  —  J  of  12  is  — 

9.  1.  Frank  bought  4  pencils  at  3  cents  each;  for  all  he 
paid  —  cents. 

2.  Mary  has  10  cents;  oranges  cost  5  cents  each;  she  can 
buy  —  oranges. 

3.  William  has  8  apples;  he  divides  them  equally  be- 
tween his  two  brothers;  each  receives  —  apples. 

4.  Anna  has  9  nuts;  she  divides  them  equally  among 
three  children;  each  child  receives  —  nuts. 

5.  Anna  has  12  roses,  and  gives  4  roses  to  each  of  her 
sisters;  she  has  —  sisters. 


6.  Make  similar  problems,  using  the  following  forms: 

2  threes  are    6.       9  is  3  threes.  One-half      of  12  is  6. 

3  fours  are  12.     10  is  5  twos.  One-third    of    9  is  3. 
8  is  4  twos.             8  is  2  fours.             One-fourth  of  12  is  3. 

Note. — This  work  is  to  be  given  in  tlie  recitation  and  under 
the  direction  of  the  teacher.  No  attempt  should  be  made  to  state 
the  process  either  in  words  or  figures.  It  is  well  to  have  children 
lay  out  the  objects  on  the  desk  and  make  their  statements  with  the 
objects  before  them.  Buttons  or  small  pasteboard  tablets  make 
convenient  counters.  In  a  problem  like  Number  5  above,  let  the 
children  lay  out  buttons  or  grains  of  corn  for  the  roses,  and 
see  that  3  fours  can  be  taken  out  of  12.  A  stick  or  tooth -pick 
might  be  placed  under  each  of  the  fours.  These  sticks  represent 
the  real  answer  to  the  problem,  the  number  of  sisters. 


THE  ONE-INCH  SQUARE  AND   THE  INCH.  7 

THE  ONE-INCH  SQUARE  AND  THE  INCH. 


One  Inch  Square. 


One  Inch. 


Three  Inches. 

10.  1 .  Cut  from  paper  a  square  which  is  one  inch  on  each 
side. 

2.  Draw  a  line  one  inch  long.     Draw  upon  the  board  a 
line  twelve  inches  long. 

Twelve  inches  are  equal  to  one  foot. 

3.  Cut  from  paper  a  measure  one  foot  in  length.     Find 
one-half  of  a  foot      One-third  of  a  foot. 

4.  Draw  a  square  which  is  two  inches  on  each  side.    How 
many  inches  is  it  around  the  square? 

5.  Cut  this  square  from  paper;  fold  it  so  as  to  show  four 
small  one-inch  squares. 

6.  Place  two  one-inch  squares  side  by  side.     Make  a 
drawing  which  is  two  inches  long,  and  one  inch  wide. 

7.  6  inches  are of  a  foot. 

8.  3  inches  are of  a  foot. 

9.  4  times  3  inches  are  —  inches. 
10.  3  times  3  inches  are  —  inches. 


8  PINTS  AND  QUARTS. 

11.  i  of  12  inches  is  —  inches. 

12.  How  much  longer  is  a  twelve-inch  line  than  a  six- 
inch  line? 

13.  How  much  longer  is  a  twelve-inch  line  than  a  nine- 
inch  line? 

14.  How  many  are  3  times  3  square  inches? 

15.  How  many  inches  is  it  around  a  square  which  meas- 
ures two  inches  on  each  side? 

16.  Julia  has  a  piece  of  ribbon  12  inches  long,  which  she 
divides  into  4-inch  pieces;  how  many  pieces  are  there? 

17.  Ella  has  a  pencil  eight  inches  long.  When  she  has 
used  3  inches,  how  many  inches  will  be  left? 

Note. — In  this  review  of  the  work  of  the  Second  Grade,  all 
exercises  must  necessarily  be  much  condensed.  Children  should 
be  familiar  with  the  one-inch  square^  the  inch  and  the  foot. 
Begin  with  the  cube  and  derive  from  it  the  one-inch  square. 
Children  should  use  these  measures  in  their  daily  work,  whenever 
opportunity  offers. 

PINTS  AND   QUARTS. 


Pint.  Quart. 

11.  1.  A  quart  of  milk  is  how  many  pints? 

2.  A  pint  is  what  part  of  a  quart? 

3.  How  many  quart  measures  can  I  fill  with  four  pints 
of  milk? 

4.  6  pints  equal  —  quarts.       6  quarts  equal  —  pints. 

5.  3  quarts  equal  —  pints.       5  quarts  equal  —  pints. 


ADDITION  AND  SUBTRACTION.  9 

6.  10  pints  equal  —  quarts.      8  pints  equal  —  quarts. 

7.  3  pints  are  how  much  more  than  a  quart? 

8.  5  pints  are  how  much  more  than  two  quarts? 

NUMBERS    THROUGH    SEVENTEEN. 

12.  Count  seventeen  by  ones. 

Write  the  names  of  the  numbers  through  seventeen. 
Begin  with  seventeen  and  name  the  numbers  in  their  order 
to  one. 

Addition  and  Subtraction. 

13.  Sums  of  any  two  numbers  through  seventeen, 

12      3      4      5      6 

12  n     10    ^    _8    _7 

13  13     13     13     13     13 

12      3      4      5      6      7 
13     12     11     10      9      8      7 


14  14  14  14  14 

14 

14 

12   3   4   5 
14  13  12  11  10 

6 
9 

7 
8 

15     15     15     15     15     15     15 

12345678 
1514131211     10    ^_8 

16  16    16     16     16    16     16    16 

12345678 
16151413121110_9 

17  17     17     17     17    17    17    17 


10  NUMBERS   THROUGH  SEVENTEEN. 

Separate  fourteen  into  two  equal  parts.  Take  away  one 
of  the  parts    what  is  left? 

Separate  fourteen  into  two  unequal  parts.  Take  away 
one  of  the  parts;  what  is  left? 

What  number  must  you  add  to  9  to  make  14? 

What  number  must  you  add  to  8  to  make  13? 

14.     1.  10  plus  3  equals  13.      2.  13  less  3  equals  10. 


10+3=13. 

13-3=10. 

7  +  6=? 

13-6=? 

6+8=? 

14-8=? 

9+5=? 

14-5=? 

5+8=? 

13-8=? 

4+9=? 

13-9=? 

8  +  3=11. 

4.  12-9=  3. 

9  +  5=14. 

13-2=11. 

7  +  7=? 

13-3=? 

5+9=? 

13-4=? 

9+4=? 

14-9=? 

8+5=? 

14-6=? 

6+7=? 

13-7=? 

Note. — Teach  the  signs  +  (plus),  —  (less),  and  =  (equals). 

5.  Find  the  sums,  giving  results  only : 

763426496 
776988554 


566957564 
838486758 


ADDITION  AND  SUBTRACTION,  H 

6.  Supply  the  numbers  omitted : 

6859467594 

14121314111413121314 

3786934798 

11131413     12     1112131413 

7.  A  man  planted  8  apple  trees  and  9  pear  trees;  how 
many  trees  did  he  plant? 

8.  I  had  14  dollars,  and  spent  9  dollars  for  a  table;  how 
many  dollars  had  I  left? 

9.  Ella  has  6  roses  and  7  violets;  how  many  flowers 
has  she? 

10.  John  had  14  cents,  and  spent  6  cents  for  a  top;  how 
much  money  had  he  left? 

11.  Make  problems  for: 

8  +  6=14  13-8  =  5  14-9  =  5  6  +  7=13 

9  +  4=13  14-6=8  12-5  =  7  12  +  2=14 

15.  Add  the  horizontal  lines  from  left  to  right,  naming 


each  sum 

(1) 

(2) 

(3) 

(4)                   (5) 

(6) 

3,2,4 

1,8,4 

2,3,8 

1,9,4          3,3,8 

1,4,9 

2,6,3 

2,7,3 

1,7,6 

2,6,5          3,4,6 

3,5,5 

3,5,4 

1,2,9 

2,6,3 

3,2,8          2,5,5 

3,9,2 

(T) 

(8) 

(S) 

(10) 

10  +  5  = 

.? 

9  +  6=? 

16-8=? 

16- 

-  9  =  ? 

7  +  8= 

=  ? 

7  +  9=? 

15-7=? 

15- 

-  8=? 

8  +  8  = 

=  ? 

6+9=? 

16-7=? 

15- 

-10=? 

9  +  8  = 

=  ? 

8+9=? 

17-9=? 

17- 

-  8=? 

12  NUMBERS  THROUGH  SEVENTEEN. 

1 1 .  Find  the  sums,  giving  results  only : 

51325384  676253433 
49682726334967585 


4 

9 

8 

6    2 

4 

2 

1     2 

3 

2    4 

12    4    3    7 

7 

2 

3 

3    4 

3 

5 

6    3 

5 

7     4 

8    6    5    4    2 

5 

3 

4 

3    4 

7 

5 

10    6 

8 

9    6 

5    7    4    9    7 

3 

9 

8 

4    5 

3 

7 

2    6 

2 

3    5 

7    4    9    5    7 

5   396848  11  11  65878  11  6 
8  10  47695   2   389798   59 


12  9765584695899637 
46879647957546784 

9697886  10  89 
7859799   678 

12.  Supply  the  numbers  omitted: 
9659867697695 

12     13     14    16     15     13     12     16     16    16     14     13     12 
56699779 


16 

13 

15 

17 

15 

15 

12 

15 

5 

8 

9 

9 

8 

8 

7 

8 

14    12     14    17     15     17     16    17 


MULTIPLICATION  AND  DIVISION.  13 

13.  Subtract  the  lower  number: 

8675689     10    87     11     12     10    876 
5432455      672      6      7      8522 


11     9     10    11     12    9     10    7     10    12     11     8     12     11 
53765231844478 


12 

10 

12 

13 

11 

14 

12 

13 

14 

11 

12 

14 

13 

9 

8 

8 

6 

5 

9 

7 

9 

8 

6 

4 

5 

8 

14 

12 

13 

14 

14 

13 

14 

11 

13 

15 

16 

15 

14 

4 

3 

4 

9 

5 

7 

6 

7 

6 

9 

7 

6 

6 

16     16     16     15     15     13     15     14 


9 

8 

5  10 

7 

8 

8 

8 

12 

16 

15  17 

17 

16 

14 

17 

7 

7 

9   9 

8 

9 

9 

8 

Multiplication  and  Division. 

16.           7X2=14  14-h2  =  7 

2X7  =  14  14^7  =  2 

8X2=16  16^2  =  8 

2X8=16  16-^-8  =  2 

5X3=15  15h-3  =  5 

3X5=15  15^5=3 


14  NUMBERS  THROUGH  SEVENTEEN, 

i  of  14=7  i  of  16  =  4 

i  of  16=8  J  of  15  =  5 

Note. — The  children  should  make  these  tables  by  means  of 
objects,  laying  down  two  sevens,  seven  twos,  etc. 

The  sign  X  is  always  read  ''multiplied  by/'  6X2=12 
is  read  ''6  multiplied  by  2  equals  12/'  2X6=12  is  read 
''2  multiplied  by  6  equals  12/' 

The  sign  -^  is  read  ''divided  by."  12^2  =  6  is  read 
"12  divided  by  2  equals  6."  12  ^6  =  2  is  read  "12  divided 
by  6  equals  2." 

17.  1.  Albert  works  in  his  garden  2  hours  each  day; 
how  many  hours  does  he  work  in  6  days? 

2.  If  a  kite  costs  8  cents,  how  many  kites  can  be  bought 
for  16  cents? 

3.  If  a  boy  rides  8  miles  an  hour  on  his  bicycle,  how  many 
hours  will  it  take  him  to  ride  16  miles? 

4.  A  lady  divided  16  pencils  equally  among  her  four 
children;  how  many  pencils  did  each  receive? 

Make  problems  orally  for: 


(5) 

(6) 

(7) 

3X5=15 

16h-8=2 

i  of  14=7 

4X4=16 

16-^2  =  8 

J  of  15=5 

2X8=16 

15-^3  =  5 

i  of  16=4 

Note. — Have  the  children  make  these  problems  in  class,  using 
objects. 


MULTIPLICATION  AND  DIVISION.  15 


18.  REVIEW. 

Note. — These  tables  may  be  used  for  oral  recitation,  the  pupil 
giving  answers  rapidly;  or  for  occupation  during  the  study 
period ;  or  for  oral  tests,  the  work  being  dictated  by  the  teacher. 


7X2  = 

3X3  = 

2X8= 

2X6= 

10  -^  2  = 

9^3  = 

8-^4  = 

10  ^5= 

3+5  = 

7  +  3  = 

3  +  4  = 

3+7  = 

16-  7  = 

16-9= 

16-8  = 

15-  8  = 

9+3  = 

6  +  4  = 

3  +  9= 

6  +  4  = 

15-  7  = 

15-  8= 

14-  5  = 

14-9  = 

4  +  8= 

3  +  8= 

2  +  6  = 

8  +  3  = 

13-  9  = 

13-  4  = 

13-  5= 

13-8= 

7  +  5  = 

4+7  = 

8  +  4  = 

9  +  7= 

13-  6  = 

13-  7  = 

3X2  = 

2X3  = 

3+7  = 

5+6  = 

5  +  7  = 

7  +  8  = 

6X2  = 

2X4= 

4X4  = 

16^8= 

8  +  8  = 

8+7  = 

9  +  5  = 

5  +  9= 

2X5  = 

3X5  = 

4X4= 

2X7  = 

7  +  9  = 

7  +  7  = 

6+9  = 

9  +  6= 

i  of  14  = 

i  of  12  = 

i  of  15  = 

iof  16  = 

12  ^3  = 

14  ^2  = 

15  4-5  = 

4X4  = 

19.  J  of  15  =  5  may  also  be  expressed:  15  -^  3  =  5,  or 
3)15.     3115  .^  ^^^^  ,,  ^g  divided  by  3  equals  5." 


5  5 

Read  the  following  and  solve : 


i  of  12=? 

12^2=? 

2)12=? 

iofl6=?      2)16=? 

J  of    8=? 

8^2  =  ? 

2)  8=? 

iofl5=?      3)15=? 

iof   9=? 

9^3=? 

3)  9=? 

io"16=?      4)16=? 

16  NUMBERS   THROUGH  SEVENTEEN. 

EXERCISE. 
20.  Give  each  answer  in  a  statement. 

1.  At  4  cents  a  yard,  what  will  3  yards  of  ribbon  cost? 
3  yards  of  ribbon,  at  4  cents  a  yard,  will  cost  12  cents. 

2.  There  are  3  rows  of  trees  in  my  yard;  in  each  row 
there  are  6  trees;  how  many  trees  are  there  in  the  yard? 

3.  Henry  rode  9  miles  in  the  morning,  and  4  miles  in  the 
afternoon;  how  many  miles  did  he  ride  in  all? 

4.  The  sum  of  two  numbers  is  8;    one  of  the  numbers 
is  2;  what  is  the  other  number? 

5.  The  sum  of  two  numbers  is  14;  one  of  the  numbers  is 
9;  what  is  the  other  number? 

6.  I  sold  a  pint  of  milk  to  each  of  four  customers;  how 
many  quarts  did  I  sell? 

7.  Mr.  Jones  sold  six  quarts  of  milk;  how  many  pints 
did  he  sell? 

8.  A  square  which  is  2  inches  on  each  side  contains  how 
many  square  inches? 


NUMBERS   THROUGH  SEVENTEEN.  17 

9.  How  many  inches  is  it  around  a  2-inch  square? 
10.  An  oblong  one  inch  wide  and  3  inches  long  contains 
how  many  square  inches? 


11.  What  is  the  distance  round  an  oblong  2  inches  wide 
and  3  inches  long? 

12.  Draw  an  oblong  2  inches  wide  and  5  inches  long. 

13.  At  6  cents  a  yard,  how  many  yards  of  lace  can  I  buy 
for  18  cents? 

14.  John  paid  15  cents  for  3  pencils;  what  did  one  pencil 
cost? 

15.  Julia  gave  away  12  pinks  to  her  sisters,  giving  3  to 
each;  how  many  sisters  had  she? 

16.  There  are  nine  boys  and  6  girls  in  Mary's  class;  how 
many  children  are  there  in  the  class? 

17.  George   had   15   cents;  he   spent   one-third  of  his 
money;  how  much  did  he  spend? 

18.  6  inches  is  half  the  length  of  John's  ruler;  what  is 
the  length  of  the  ruler? 

19.  5  cents  is  one-third  of  what  I  paid  for  a  box  of 
berries;  what  did  I  pay  for  the  berries? 

20.  I  have  9  cents;  how  many  cents  must  I  add  to  it  to 
make  15  cents? 


18  NUMBERS  FROM   TEN   TO   TWENTY. 

NUMBERS  FROM  TEN  TO  TWENTY,  AS  TENS  AND 

ONES 

21.  Note. — Use  tooth-picks,  shoe-pegs,  or  any  available  ob- 
jects for  this  illustration  work. 

nUJIII     Ten  ones  are  one  ten. 


fli 
III 
1111 


One  ten  and  one  one  are  eleven. 
10     and       1       are     11. 

One  ten  and  two  ones  are  twelve, 
10     and       2        are      12. 

One  ten  and  three  ones  are  thirteen, 
10     and  3        are      13. 


One  ten  and  four  ones  are  fourteen. 
10     and         4        are      14. 

One  ten  and  five  ones  are  fifteen, 
10     and       5        are     15. 

One  ten  and  six  ones  are  sixteen, 
10     and      6        are      16. 


One  ten  and  seven  ones  are  seventeen. 
10     and  7        are        17. 

One  ten  and  eight  ones  are  eighteen. 
10     and         8        are      18. 

One  ten  and  nine  ones  are  nineteen. 
10     and        9        are      19. 


WRITING  NUMBERS  TO  TEN,  19 

Two  tens  are  twenty, 
2    tens  are    20. 

23.  1.  Eleven  is  how  many  tens  and  how  many  ones? 
Which  figure  in  the  number  11  stands  for  the  one?  Which 
figure  stands  for  the  one  ten? 

2.  Write  the  numbers  from  one  to  ten  in  a  column. 

3.  Write  the  numbers  from  ten  to  twenty  in  a  column. 

4.  Which  figure  always  stands  for  the  ones,  when  ones 
and  tens  are  written?     (The  right  hand  figure.) 

5.  Which  figure  in  the  number  18  stands  for  ones?  Which 
stands  for  the  tens? 

6.  Which  figure  stands  for  the  tens  in  the  number  20? 
Which  figure  stands  for  ones?    0  is  called  nought  or  zero. 

WRITING  NUMBERS    TO   TEN. 

23.  The  letters  I  (one),  V  (five),  and  X  (ten),  are  also 
used  to  represent  numbers. 

Numbers  to  10  are  represented  in  three  different  ways, 
as  follows : 

Wovds.'    zero,  one,   two,    three,     four,     five,      six,        seven,     eight,   nine,     ten. 

Figures:  012       3       456        7        89     10 
Letters :        I     II     III     IV     V     VI     VII  VIII  IX     X 

THE  NUMBERS  EIGHTEEN,  NINETEEN,  AND  TWENTY. 
34.  Write  the  names  of  the  numbers  from  one  to  twenty. 
Sums  of  any  two  numbers  through  tiventy. 
123456789 

17  16     15     14     13     12     n     10    ^ 

18  18    18    18    18    18    18    18    18 


20    NUMBERS  EIGHTEEN,  NINETEEN,  AND  TWENTY, 

123456789 
181716151413121110 

19     19     19     19     19     19     19     19     19 

12      3      4      5      6      7      8 

19  18  171615141312 

20  20  20  20  20  20  20  20 

Add  these  columns,  beginning  at  the  top  and  naming 
each  sum : 

975886425442 
660514871255 
139165187526 

211241376744 
8594. 3  7940687 
778769427689 


675978893 
698698628 
823223697 

7  10  12  112  2  3  2 

8  1110  9  112  3  5 
09867596796 
18756478534 

13  11112  2  3  12 
43494436864 
89867987698 
54534543243 

Add  the  columns  above,  beginning  at  the  bottom. 


COMPARISON  OF  HALVES  AND  FOURTHS. 


21 


Note.— In  addition  and  all  other  arithmetical  processes,  ac- 
curacy should  be  the  first  consideration.  A  reasonable  degree  of 
rapidity  may  be  acquired  by  practice. 


COMPARISON  OF  HALVES  AND  FOURTHS. 


25.  1.  A  whole  melon  can  be  divided  into  how  many- 
halves?     How  many  fourths? 

2.  Fold  a  paper  square  into  two  equal  oblongs.  One  of 
the  oblongs  is  what  part  of  the  square? 

3.  Fold  the  same  square  into  two  equal  triangles.  One 
of  the  triangles  is  what  part  of  the  whole  square? 

4.  In  one  whole  there  are  how  many  halves? 

5.  Fold  a  paper  square  so  as  to  make  four  small  squares 
of  equal  size.  One  of  these  small  squares  is  one-fourth  of 
the  whole. 

In  one  whole  there  are  how  many  fourths? 

6.  One  half  of  the  square  is  how  many  fourths? 

7.  If  you  should  fold  down  one  half  of  the  large  square, 
how  many  fourths  would  remain? 


22  COMPARISON  OF  HALVES  AND  FOURTHS. 

26.  From  the  circles  on  page  21,  find  answers  to  the 
following  questions: 

(1)  (2) 

i  +  i=?  i— i  =  how  many  fourths? 

J  +  i=?  |— i  =  how  many  fourths? 

|  +  i=?  4  —  i=  how  many  fourths? 

|  +  i=  ?  |— J  =  how  many  fourths? 

(3) 


(3) 

{  is  contained  in  J,  —  times. 
\  is  contained  in  f ,  —  times. 
i  of  i  =  how  many  fourths? 
iX4=  how  many  fourths? 
J  X  3  =  how  many  fourths? 


4.  Frank  has  half  an  orange,  and  Edwin  one-fourth  of 
an  orange;  they  both  together  have  —  fourths  of  the 
orange. 

5.  George  ate  one-fourth  of  a  pie;  there  were  remaining 
of  the  pie. 

6.  There  are  three-fourths  of  a  bushel  of  apples  in  one 
barrel,  and  one-fourth  in  another;  in  both  barrels  there 
is  — . 

7.  Jennie  had  an  apple  and  gave  away  one-fourth  of  it; 
she  had  left. 

EXERCISE. 

27.  Write  the  answers  in  statements. 

1.  Frank  has  8  pigeons,  3  red  birds,  and  4  canaries;  how 
many  birds  has  he? 

Frank  has  15  birds. 


EXERCISE.  23 

2.  Helen  used  16  eggs  in  making  4  cakes;  how  many  eggs 
did  she  put  into  each  cake? 

3.  Mary  drew  four  leaves  on  each  of  the  four  sides  of  her 
box;  how  many  leaves  did  she  draw? 

4.  Fanny  had  19  shells;  before  she  reached  home  she  lost 
5  of  them;  how  many  had  she  left? 

5.  Jennie  sewed  6  buttons  on  her  shoes,  and  had  9 
buttons  left;  how  many  had  she  at  first? 

6.  Each  of  my  3  brothers  gave  me  6  cents;  how  much 
money  did  all  give  me? 

7.  At  15  cents  a  yard,  what  must  I  pay  for  one-third  of 
a  yard  of  ribbon? 

8.  After  spending  10  cents  for  paints,  Frank  had  5  cents 
left;  how  much  money  had  he  at  first? 

9.  When  milk  is  6  cents  a  quart,  how  much  must  you  pay 
for  a  pint? 

10.  Four  children  each  spent  5  cents  for  car-fare;  how 
much  money  did  they  all  spend? 

11.  ISboys  were  coasting;  there  were  three  boys  on  each 
sled;  how  many  sleds  were  there? 


a  D  D  D  D  D 


Read  the  problem  and 
the  answer  from  tlie  pic- 
ture. 


12.  At  3  cents  each,  how  many  pencils  can  I  buy  for 
18  cents? 

13.  At  3  cents  a  pint,  what  will  4  pints  of  milk  cost? 

14.  4  pints  are  how  many  quarts? 

15.  12  pints  are  how  many  quarts? 


24  EXERCISE. 

16.  Draw  an  oblong  3  inches  by  4  inches;  how  many 
square  inches  are  there  in  the  surface? 

17.  Divide  an  apple  equally  among  4  boys;  what  part 
does  each  boy  receive? 

18.  George  divided  a  melon  into  four  equal  parts,  and 
gave  away  three  of  the  parts;  what  part  of  the  melon  did 
he  keep  for  himself? 

19.  Henry  wishes  to  visit  his  cousin  who  lives  17  miles 
away;  after  riding  8  miles  how  much  farther  has  he  to  go? 

20.  Anna,  Carl,  and  Fred  went  nutting  and  gathered  12 
quarts  of  nuts;  if  they  divided  them  equally,  what  part 
did  each  receive? 


CHAPTER  II. 


NUMBERS  FROM  TWENTY  TO  ONE  HUNDRED,  AS 
TENS  AND  ONES. 

2  8.  Write  the  numbers  from  ten  to  twenty. 
Which  figures  always  stand  for  ones? 

Two  tens  are  twenty — 20. 
Three  tens  are  thirty — 30. 
Four  tens  are  forty — 40. 
Five  tens  are  fifty — 50. 
Six  tens  are  sixty — 60. 

Seven  tens  are  seventy — 70. 
Eight  tens  are  eighty — 80. 
Nine  tens  are  ninety — 90. 

Ten  tens  are  one  hundred — 100. 


26      NUMBERS  FROM   TWENTY  TO  ONE  HUNDRED. 


29.  Two  tens  and  one  one  are  twenty-one — 21. 


Two  tens  and  two  ones  are  twenty-two — 22. 
Two  tens  and  three  ones  are  twenty-three — 23. 
Two  tens  and  four  ones  3,re  twenty-four — 24. 
Two  tens  and  five  ones  are  twenty-jive — 25. 

Two  tens  and  six  ones  are  twenty-six — 26. 

Two  tens  and  seven  ones  are  twenty-seven 
-27. 

Two  tens  and  eight  ones  are  twenty-eight 

-28. 

Two  tens  and  nine  ones  are  twenty-nine 
-29. 

Three  tens  are  thirty — 30. 


30.  1.  Count  by  ones  from  thirty  to  forty. 

2.  Read  these  numbers:  31,  32,  33,  34,  35,  36,  37,  38, 
39,  40. 

3.  Write  the  above  numbers  in  a  column  and  name  the 
ones. 


WRITING  NUMBERS  FROM  TEN  TO  THIRTY,        27 
4.  Read  the  following  numbers : 


40 

50 

60 

70 

80 

90 

41 

51 

61 

71 

81 

91 

42 

52 

62 

72 

82 

92 

43 

53 

63 

73 

83 

93 

44 

54 

64 

74 

84 

94 

45 

55 

65 

75 

85 

95 

46 

56 

66 

76 

86 

96 

47 

57 

67 

77 

87 

97 

48 

58 

68 

78 

88 

98 

49 

59 

69 

79 

89 

99 
100 

5.  How  many  ones  are  there  in  69?    How  many  tens  and 
how  many  ones  in  69? 

6.  Which  is  more,  83  or  74?    92  or  89? 

7.  Arrange  these  numbers  in  order:  70,  65,  69,  67,  66, 
64,  68. 

8.  Arrange  these  in  order:  81,79,83,78,80,82,77. 

WRITING  NUMBERS  FROM  TEN  TO  THIRTY. 

31.  Numbers  from  10  to  30  are  represented  by  words, 
figures  and  Roman  characters,  as  follows : 

Ten         Eleven       Twelve      Thirteen     Fourteen     Fifteen       Sixteen 


10 

11        12 

13 

14       15 

16 

X 

XI      XII 

XIII 

XIV     XV 

XVI 

Seventeen 

Eighteen 

Nineteen 

Twenty 

Twenty- one 

17 

18 

19 

so 

21 

XVII 

XVIII 

XIX 

XX 

XXI 

28 


ADDITION  AND  SUBTRACTION. 


Twenty-two      Twenty-three         Twenty-four          Twenty-five 

Twenty-six 

22              28              24              25 

26 

XXII        XXIII         XXIV         XXV 

XXVI 

Twenty-seven             Twenty-eight             Twenty-nine 

Thirty 

27                  28                  29 

30 

XXVII         XXVIII          XXIX 

XXX 

The  Roman  characters  are  not  now  employed  in  number 
work,  but  are  chiefly  used  for  numbering"  chapters  and  lessons. 
They  are  used  also  to  indicate  the  ditt'ercnt  volumes  of  a  series  of 
books,  and  to  mark  the  hours  on  the  dials  of  clocks  and  watches. 

Write  the  numbers  31  to  39  in  Roman  characters. 
Read  the  following: 


VII 

XIX 

XV 

XVI 

XVIII 

IX 

XXIX 

XXV 

XXIV 

XXIII 

XI 

XXXIX 

XXXV 

XXXVII 

XXXIV 

ADDITION  AND   SUBTRACTION. 

32.  Give  sums  at  sight,  adding  by  tens : 

Thus,  in  adding  20  and  12  say:  20  and  10  are  30,  and  2  are  32. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(•7) 

20 

30 

40 

50 

60 

70 

80 

12 

12 

12 

12 

12 

12 

12 

(8) 

(9) 

(10) 

(11) 

(12) 

(13) 

(14) 

21 

31 

41 

51 

61 

71 

81 

12 

12 

12 

12 

12 

12 

12 

ADDITION  AND  SUBTRACTION.  29 


(15) 

(16) 

(17) 

(18) 

(19) 

(20) 

(21) 

21 

31 

41 

51 

61 

71 

81 

14 

14 

14 

14 

14 

14 

14 

(22) 

(23) 

(24) 

(25) 

(26) 

(27) 

(28) 

24 

34 

44 

54 

64 

74 

84 

15 

15 

15 

15 

15 

15 

15 

Add  the  same  numbers,  giving  the  sum  of  the  ones  and 
then  the  sum  of  the  tens. 

33.  Add  12, 49,  and  33. 

12  Add  the  ones  first,  naming  results  only ;  thus:  3,  12, 

AQ  14  ones  (1  ten   and  4  ones).      Write  the  4  ones  in 

ones'  place  below  the  line,  and  add  the  1  ten  with 

the  tens.     4,  8,  9  tens.     Write  9  tens  in  tens'  place. 

94    The  sum  is  94. 

Copy  and  add : 

(1)   (2)   (3)   (4)  (5)  (6)  (7)   (8)  (9)  (lO) 

12  25  36  44  16  29  34  28  25  19 
14  10  11  14  25  16  23  16  26  52 
16  12  14  10  12  11  39  51  33  22 

(11)  (12)  (13)  (14)  (15)  (16)  (17)  (18)  (19)  (20) 

28  39  28  18  29  67  58  45  19  35 

16  14  26  54  14  17  13  16  52  13 

2   3  13  17  23   2  ^  14  26  48 

(21)  (22)  (23)  (24)  (25)  (26)  (27)  (28)  (29)  (30) 

19  17  25  38  48  36  14  12  25  24 
26  26  10  25  11  14  28  27  31  12 
31  33  29  31  26  35  31  28  47  45 


30  ADDITION  AND  SUBTRACTION. 

(31)   (32)  (33)   (34)  (35)   (36)  (37)   (38)  (39)  (40) 

23  28  14  22  42  41  32  21  84  21 
10  10  15  18  15  25  14  39  13  37 
28252237363747182619 

34.  Find  differences,  subtracting  by  tens: 

Thus,  in  subtracting  12  from  36,  say:  36  less  10  =  26  ;  26  less 
2  =  24. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

36 

47 

58 

69 

75 

86 

94 

10 

10 

10 

10 

10 

10 

10 

(8) 

(9) 

(10) 

(11) 

(12) 

(13) 

(14) 

36 

47 

58 

69 

75 

86 

94 

12 

12 

12 

12 

12 

12 

12 

(15) 

(16) 

(17) 

(18) 

(19) 

(20) 

(21) 

36 

47 

58 

69 

75 

86 

94 

14 

14 

14 

14 

14 

14 

14 

(22) 

(23) 

(24) 

(25) 

(26) 

(27) 

(28) 

36 

47 

58 

69 

75 

86 

94 

20 

20 

20 

20 

20 

20 

20 

(29) 

(30) 

(31) 

(32) 

(33) 

(34) 

(35) 

46 

65 

79 

54 

93 

88 

37 

22 

22 

22 

22 

22 

22 

22 

(36)        (37)        (38)        (39)        (40)        (41)        (42) 

57    49    65    74    87    95    46 
23    23    23    23    23    23    23 


QUARTS  AND  GALLONS. 


31 


[43) 

(44) 

(45) 

(46) 

(47) 

(48) 

(49) 

64 

75 

39 

88 

95 

57 

46 

24 

24 

24 

24 

24 

24 

24 

QUARTS  AND   GALLONS. 


Quart. 


Gallon. 


35.  1.  It  takes  4  quarts  to  fill  a  gallon  measure;  one 
quart  is  what  part  of  a  gallon? 

2.  Two  quarts  are  what  part  of  a  gallon? 

3.  Eight  quarts  are  how  many  gallons? 

4.  Two  gallons  are  how  many  quarts? 

5.  Five  quarts  are  how  much  more  than  a  gallon? 

6.  A  gallon  and  two  quarts  are  how  many  quarts? 

7.  I  bought  a  gallon  of  milk  on  Tuesday,  and  half  a 
gallon  on  Wednesday;  how  many  quarts  did  I  buy? 

8.  A  man  sells  a  quart  of  milk  to  each  of  ten  customers; 
how  many  gallons  does  he  sell? 

9.  Sixteen  quarts  are  how  many  gallons? 

10.  Two  and  one-half  gallons  are  how  many  quarts? 

2  pints  (pt.)  =  1  quart  (qt.). 
4  quarts       =  1  gallon  (gal.). 


32  MULTIPLICATION  AND  DIVISION. 

MULTIPLICATION  AND   DIVISION. 


36. 

REVIEW. 

(1) 

(2) 

(3) 

(4) 

1X2=? 

6X  2=? 

2h-2=? 

12^  2=? 

2X2=? 

7X  2=? 

4h-2  =  ? 

14^  2=? 

3X2=? 

8X  2=? 

6^2=? 

16^  2=? 

4X2=? 

9X  2=? 

8^2=? 

18^  2=? 

5X2=? 

lOX  2=? 

10^2=? 

20^  2=? 

2X1=? 

2X  6=? 

6-^3=? 

12 -^  6=? 

2X3=? 

2X  7=? 

10^5=? 

14^  7=? 

2X4=? 

2X  9=? 

16h-8  =  ? 

18^  9=? 

2X5=? 

2X10=? 

8h-4  =  ? 

20^-10=? 

37.  Copy  and  learn: 

11 X  2  =  22 

22^  2= 

11 

12X  2=24 

24-  2  = 

12 

2X11  =  22 

22  4-11  = 

:       2 

2X12  =  24 

24h-12= 

:       2 

EXERCISE. 

38.  1.  At  2  cents  each,  what  will  11  pen-holders  cost? 

2  cents  X 11  =  22  cents 

11  pen-holders  will  cost  22  cents. 

2.  If  a  man  earns  2  dollars  a  day,  how  much  will  he  earn 
in  12  days? 

3.  Mary  wishes  to  buy  some  flowers  for  her  mother's 


MULTIPLICATION  AND  DIVISION.  33 

birthday;  if  she  buys  pinks  at  2  cents  apiece,  how  many  can 
she  buy  for  22  cent  J? 

22  cents  ^2  cents  =  11 
Mary  can  buy  11  pinks. 

Read  the  problem,  and  give  the  answer  from  the  picture. 

f   ^    f   f  ^  ^  <f  ^  'f   f>   ^ 

4.  At  2  cents  each,  how  many  pencils  can  you  buy  for 
24  cents? 


39. 

REVIEW 

(1) 

(2) 

(3) 

(4) 

2X3=? 

5X3=? 

6^3=? 

12 --3=? 

3X3=? 

3X5=? 

9^3=? 

15^3=? 

4X3=? 

6X3=? 

18-^3=? 

15^5  =  ? 

3X4  =  ? 

2X6=? 

6h-2=? 

12 -=-4=? 

40.  Copy  and  learn: 


7X3  =  21 

10X3=30 

21^3=7 

30- 

^3=10 

8X3  =  24 

11X3=33 

24-^3  =  8 

33- 

^3=11 

9X3=27 

12X3=36 

27-^3=9 

36- 

^3=12 

3X7  =  21 

3X10=30 

21^7=3 

30- 

^10=3 

3X8=24 

3X11  =  33 

24^8=3 

33- 

Hll  =  3 

3X9=27 

3X12=36 

27^-9=3 

36- 

hl2=3 

34  MULTIPLICATION  AND  DIVISION. 

EXERCISE. 

41.  In  the  written  work^  give  figures  and  statements. 

1.  John  bought  7  peaches  and  paid  3  cents  apiece;  how 
much  money  did  he  spend? 

3  centsX7  =  21  cents.     John  spent  21  cents. 

2.  At  3  cents  each,  how  many  oranges  can  I  buy  for  24 
cents?     (Make  a  picture.) 

3.  What  will  9  chairs  cost,  at  3  dollars  each? 

4.  How  long  does  it  take  a  man  to  earn  27  dollars,  if  he 
earns  3  dollars  a  day? 

5.  In  going  to  school  and  returning,  George  walks  3  miles 
each  day;  how  far  does  he  walk  in  12  days? 

6.  Helen  learned  3  new  words  each  day  for  11  days;  how 
many  words  did  she  learn? 

7.  Make  problems  for: 

7X3  =  21  18^3=  6  6X3=18 

9X3  =  27  12X3=36  12X2  =  24 

24-3=   8  33-^3=11  18-^2=  9 

Note. — This  work  should  be  done  in  the  recitation  period  and 
under  the  direction  of  the  teacher,  the  children  first  laying  out 
the  objects  for  each  problem,  or  making  the  picture. 

8.  Write  the  multiplication  table  of  3's  from  2X3  to 
12X3. 

9.  Recite  the  table  of  3's  from  memory. 

10.  Write  the  table  from  3X2  to  3X12,  and  recite  it. 

11.  Beginning  with  3,  count  by  3's  to  36. 

12.  Beginning  with  36,  subtract  by  3's  to  0. 


MULTIPLICATION  AND  DIVISION.  35 

43.  Copy  and  learn : 

2X4==   8  5X4  =  20  8X4=32  11X4=44 

3X4=12  6X4  =  24  9X4=36  12X4=48 

4X4=16  7X4  =  28  10X4=40 

Write  these  by  placing  4  first.     Thus,  4X2=   8, 

4X3=12,  etc. 

Recite  the  division  table,  from  the  multiplication  table. 

Thus,  2X4=8;  8-^4  =  2,         3X4=12;  12-4=3, 

and  8^2  =  4.  and  12 --3  =  4,  etc. 

EXERCISE. 
4:3.  Twelve  things  make  a  dozen. 

1.  How  many  cakes  can  be  made  from  a  dozen  eggs,  if  4 
eggs  are  used  for  each  cake? 

2.  If  there  are  4  desks  in  a  row,  how  many  desks  are  there 
in  7  rows? 

3.  At  4  dollars  each,  what  will  8  hats  cost? 

4.  How  many  gallon  measures  can  be  filled  from  a  can 
which  holds  36  quarts? 

5.  What  will  12  chairs  cost,  at  4  dollars  each? 

6.  Frank  is  32  miles  away  from  home ;  if  he  walks  at  the 
rate  of  4  miles  an  hour,  how  long  will  he  be  in  reaching 
home? 

7.  I  put  28  quarts  of  oil  into  lamps  holding  4  quarts  each; 
how  many  lamps  can  I  fill?     (Make  a  picture.) 

8.  9  gallons  are  how  many  quarts? 

9.  How  many  quart  cans  will  be  needed  to  hold  9  gallons 
of  maple  molasses? 


36  MULTIPLICATION  AND  DIVISION, 

10.  Make  problems  for: 

6X4  =  24  9X4  =  36        48^4  =  12 

11X4  =  44  8X4  =  32        28^-4-  7 

40h-4=10        36-^4=  9  7X4  =  28 

Note. — This  should  be  done  in  class. 

11.  Begin  with  4  and  count  by  4^s  to  48. 

12.  Begin  with  48  and  subtract  by  4^s  to  0. 

13.  Give  answers  at  sight: 
Thus :  7  multiplied  by  4  equals  28. 

7X4  12X4  7X3  11x4  12X3  3X  9  4X12  3X  7 
9X3  8X3  6X4  9X2  9X4  3X12  3X  8  3X11 
6X3   8X4  12X2   9X3   9X3  2X  9  4X  7  4X11 

14.  Among  how  many  boys  can  12  oranges  be  divided,  if 
each  boy  receives  4  oranges? 

This  result  may  be  stated  in  two  ways : 
12  oranges ^4  oranges  =  3;  or,  4  oranges)12  oranges 

~~3 

They  can  be  divided  among  3  boys. 

15.  Read  at  sight: 

4  apples)24  apples    4  roses) 48  roses        3  books) 36  books 
6  "^^^^^  ^^^ 

4  nails) 36  nails  3  pencils)21  pencils  4  gallons)44  gallons 
4  pints) 32  pints      3  lemons)24  lemons    3  dollars)27  dollars 


FINDING  ONE  OF  THE  EQUAL  PARTS  OF  A  NUMBER.  37 

Finding  One  of  the  Equal  Parts  of  a  Number. 

44.  I  wish  to  divide  21  nuts  equally  among  three  chil- 
dren; how  many  nuts  will  each  receive? 

We  count  off  one  to  each  child  in  turn,  until  we  have  given 
away  all  the  nuts. 


First  child,  ©©©©©©© 
Second  child,  ©©©©©©© 
Third  child,      ©©•©©©©© 

J  of  21  nuts  is  7  nuts. 

Each  child  will  receive  7  nuts. 

EXERCISE. 

45.  1.  Divide  21  apples  equally  among  3  children.  How 
many  apples  will  each  receive?  (Make  a  picture,  and  give 
figures  and  statement.) 

2.  Divide  27  shells  equally  among  3  children;  how  many 
will  each  receive? 

3.  Divide  28  roses  equally  among  4  sisters;  how  many 
will  each  receive? 

4.  A  gardener  takes  24  plants  to  market  and  sells  one- 
third  of  them;  how  many  does  he  sell? 

5.  Frank  had  30  cents  and  spent  ^  of  his  money  for  a  top; 
how  many  cents  did  he  spend? 


38  FINDING  ONE  OF  THE  EQUAL  PARTS  OF  A  NUMBER. 

6.  Divide  23  apples  equally  between  two  boys.     How 
many  will  each  receive? 

First  boy,  OOOOOOOOOOOO 

Second  boy,      OOOOOOOOOOOO 
i  of  23  apples  equals  11 J  apples. 
'    Each  boy  receives  11^  apples. 

7.  Henry  paid  25  cents  for  two  pounds  of  butter;  what  is 
the  cost  of  one  pound? 

8.  Divide  21  pears  equally  among  4  children.     What  part 
of  all  the  pears  will  each  receive? 

How  many  pears  will  each  receive?     (Make  a  picture.) 

9.  I  had  40  cents  and  spent  J  of  it  for  a  yard  of  muslin; 
how  much  did  I  spend? 

10.  John  has  a  tape  measure  36  inches  in  length;   one- 
third  of  the  measure  is  how  many  inches? 

11.  If  I  divide  a  melon  among  three 
boys,  so  that  their  shares  are  equal,  what 
part  of  the  melon  does  each  boy  receive? 

12.  Divide  16  cakes  equally  among  3  playmates;  how 
many  cakes  will  each  receive? 

First,  O  O  O  O  O  ^ 
Second,  O  O  O  O  O  ^ 
Third,       O  O  O  O  O  ^ 

13.  Find  J  of  10, 15, 16, 18, 19,  21,  24, 25, 28  and  36. 

14.  Find  J  of  all  numbers  from  12  to  25. 

15.  Find  i  of  16, 17, 20, 21, 24, 28, 32  and  36. 


FINDING  ONE  OF  THE  EQUAL  PARTS  OF  A  NUMBER.  39 


16.  Make  problems  for : 

J  of  15  =  5        i  of  24  =  6  i  of  21  =  7 

J  of  18  =  6        i  of  30  =  10        i^ofl9  =  6J 

Note, — To  be  done  in  class. 

Here  are  two  ways  by  which  we  may  express  the  finding 
of  one  of  the  three  equal  parts  of  18  dollars. 


J  of  18  dollars  =  6  dollars. 

3)18  dollars 

6  dollars 

17.  Give  answers  at  sight: 

3)18  cents 

4)36  inches 

3)28  pencils 

cents 

inches 

pencils 

2)24  apples 

3)30  yards 

4)32  roses 

apples 

yards 

roses 

3)21  nuts 

2)25  apples 

4)48  dollars 

nuts 

apples 

dollars 

46. 

REVIEW. 

1X2=  2 

1X3=  3 

1X4=  4 

2X2=  4 

2X3=  6 

2X4-  8 

3X2=  6 

3X3=  9 

3X4=12 

4X2=  8 

4X3  =  12 

4X4  =  16 

5X2  =  10 

5X3  =  15 

5X4  =  20 

6X2  =  12 

6X3  =  18 

6X4  =  24 

7X2  =  14 

7X3  =  21 

7X4  =  28 

8X2  =  16 

8X3  =  24 

8X4  =  32 

9X2  =  18 

9X3  =  27 

9X4  =  36 

10X2  =  20 

10X3  =  30 

10X4  =  40 

r      11X2  =  22 

11X3  =  33 

11X4  =  44 

12X2  =  24 

12X3  =  36 

12X4  =  48 

Write  these  tables  with  the  2's,  3's  and  4's  first. 


40  EXERCISE. 


EXERCISE. 


47.  1.  On  Monday  Albert  had  30  cents  in  his  savings 
bank;  on  Tuesday  he  earned  10  cents  by  selUng  papers. 
How  much  money  had  he  then? 

2.  George  had  24  cents  and  spent  6  cents  for  an  orange; 
how  many  cents  had  he  left? 

24  cents  —  6  cents  =  18  cents. 
George  had  18  cents  left. 

3.  Frank  paid  24  cents  for  a  kite  and  6  cents  for  a  top; 
how  much  more  did  he  pay  for  the  kite  than  for  the  top? 

24  cents  —  6  cents  =  18  cents. 

Frank  paid  18  cents  more  for  the  kite  than  for  the  top. 

4.  Robert  had  3  dozen  nails  and  gave  one  dozen  to 
Henry ;  how  many  dozen  had  he  left?  How  many  nails  had 
he  left? 

5.  Margaret  gathered  28  pond-lilies  and  Mabel  gathered 
10;  how  many  did  both  gather? 

6.  A  boy  having  40  cents,  paid  8  cents  for  a  ball;  how 
many  cents  had  he  then? 

7.  Grace  wrote  11  lines  in  her  copy-book  on  Monday,  6  on 
Tuesday  and  3  on  Wednesday;  how  many  lines  did  she 
write  in  all? 

8.  Mary  wishes  to  buy  a  picture  which  costs  25  cents ;  she 
has  only  10  cents.  How  many  more  cents  must  she  have  to 
buy  the  picture? 

9.  One  week  a  chair-maker  made  2  dozen  parlor  chairs 
and  8  office-chairs.  How  many  chairs  did  he  make  in  the 
week? 


EXERCISE.  41 

10.  Alfred  had  40  cents;  he  paid  9  cents  for  pencils;  how 
many  cents  had  he  then? 

11.  A  grocer  bought  4  dozen  boxes  of  strawberries;  he 
sold  one  dozen  boxes.     How  many  boxes  had  he  left? 

12.  Eight  gallons  are  how  many  quarts? 

13.  If  8  quarts  of  cider  are  sold  from  an  8-gallon  cask, 
how  many  quarts  are  left? 


CHAPTER  III. 

READING  AND  WRITING  NUMBERS:  HUNDREDS 

One  Hundred  to  Five  Hundred. 

48.  Take  counters  and  find  1  hundred,  2  tens,  4  ones. 
Write  the  number. 

Note. — Use  toothpicks  or  shoe-pegs,  as  heretofore  suggested. 
Find  with  the  counters  and  write : 
1  hundred,  3  tens,  7  ones.  1  hundred,  9  tens,  0  ones. 

^  a  5      a       g      u  ^  u  Q      u      ^      u 

1        ^'        8    ^^     3    ^^  1         "       1    ^<     lone. 

How  many  ones  are  there  in  the  first  number?  How 
many  ones  in  each  of  the  other  numbers? 

Begin  with  1  hundred,  and  write  in  figures  all  the  num- 
bers through  1  hundred,  9  tens,  and  9  ones. 

Add  1  to  199;  how  many  tens  have  you?  How  many 
ones?  Write  the  number. 

49.  What  does  the  figure  4  mean  in  the  num-  134 
ber  134?  Because  the  figure  4  means  4  ones,  it  216 
is  written  in  ones^  place.  For  what  do  the  6,  9,  |^^ 
and  8  stand? 

5  and  7  stand  for  what?    They  are  written  in  tens^  place. 
The  figure  1  in  the  first  number  means  what?    The 
figure  2  in  the  second  number  means  what? 


READING  AND  WRITING  NUMBERS:  HUNDREDS.     43 

Because  the  figure  1  means  one  hun-         Period  of  ones. 
dred,  it   is  written  in   hundreds^  place.   Hundreds'  Tens'    ones' 

'  ^      ^  place.   place,  place. 

In  what  place  is  the  figure  2  written?  13        4 

Hundreds  are  always  written  in  hun-         2        16 

dreds^  place,  tens  in  tens'  place,  and  ones         15        9 

in  ones'  place. 
Ones^  place,  tens'  place,  and  hundreds'  place  make  the 

period  of  ones. 

50.  1.  Copy  and  read  these  numbers: 

124        101         116         173         119  112 

186         111         105         113         191  121 

210         198         115         131         109  200 

181         106         137         103         129  201 

2.  Find  with  the  counters  and  write  the  numbers  from 
200  to  300. 

3.  Write  in  figures: 

2  hundreds,  5  tens,  3  ones.       3  hundreds,  0  tens,  0  ones. 
4         ''         6    "     7    "  3        ''  2    ''    2    '' 

3  "         7    ^^     9    ^^  5        "  0    "     0    '' 

4.  The  first  number  equals  how  many  ones? 

5.  Which  is  greater,  3  hundred  or  3  tens? 

6.  5  hundred  is  how  many  more  than  3  hundred? 

7.  Read  the  following : 

311  222  202 

210  333  212 

413  331  221 

125  313  211 

8.  '414  is  how  many  more  than  313?     330  is  how  many 
more  than  230?    450  is  how  many  less  than  500? 


314 

384 

404 

341 

448 

401 

413 

444 

309 

431 

414 

319 

44     READING  AND  WRITING  NUMBERS:  HUNDREDS. 

Five  Hundred  to  One  Thousand. 

51.  1.  Find  with  the  counters  5  hundreds,  9  tens,  and  9 
ones.     Add  one  one.     How  many  hundreds  have  you? 

2.  Write  in  figures   6   hundreds.     Write   6  hundreds, 
4  tens;  6  hundreds,  5  tens,  and  2  ones. 

3.  Find  7  hundreds.    Write  the  number  in  figures. 

4.  Read: 


643 

611 

721 

505 

707 

606 

751 

610 

712 

689 

770 

660 

589 

601 

702 

799 

777 

666 

5.  Which  is  the  greater  number,  659  or  569?    697  or 
769?    571  or  751? 

6.  Find  8  hundreds,  8  tens,  and  8  ones. 

7.  Find  9  hundreds,  and  represent  the  number  by  figures. 

8.  Find  9  hundreds,  9  tens,  and  9  ones. 
9.- Read: 


845 

984 

901 

991 

999 

880 

862 

936 

909 

919 

808 

881 

933 

847 

990 

900 

888 

818 

52.  The  greatest  number  that  can  be  expressed  by 
three  figures  is  999. 

Add  1  to  999;  how  many  hundreds  have  you?  Ten 
hundreds  make  1  thousand. 

The  number  one  thousand  is  expressed  by  writing  the 
figure  1  in  thousands'  place,  to  the  left  of  the  hundreds; 
thus,  1,000. 

Ten  hundreds  equal  one  thousand. 


ADDITION.  45 

ADDITION.  . 

EXERCISE. 

53.   (a)  Add  at  sight,  naming  each  sum: 
(b)  Copy  and  find  the  answers: 

(1)   (2)  (3)   (4)  (5)  (6)   (7)  (8)   (9) 

31  27  20  11  12  31  51  12  32 
21  18  31  41  50  19  21  41  12 
29  40  28  16  17  25  19  16  27 
383127251634171815 

(10)  (11)  (12)  (13)  (14)  (15)  (16)  (17)  (18) 

23  12  13  51  31  61  41  32  62 
23  25  23  14  29  14  24  43  16 
19  16  39  18  46  17  59  5S  17 
234424254324351453 

(19)  (20)  (21)  (22)  (23)  (24)  (25)  (26)  (27) 

13  51  82  13  41  79  54   8  14 

58  36  14  48  36  10  26  25  36 

66  49  28  66  49  28   7  92  27 

42  3443433443531482 

(28)  (29)  (30)  (31)  (32)  (33)  (34)  (35)  (36) 

79  99  89  38  38  97  38  56  2 

13  03  13  04  16  49  17  57  12 

66  25  25  72  72  21  82  23  49 

21  51  41  62  52  11  41  41  63 

11  11  12  13  12  11  12  11  93 


46  SUBTRACTION 

(37)   (38)  (39)   (40)  (41)   (42)   (43)  (44)   (45) 

76  36  55  51  50  98  71  72  34 
64  34  24  34  59  57  15  45  75 
23  73  75  72  34  12  64  41  22 
12  33  21  14  31  12  25  16  12 
121111191110191557 

54.  Finding  the  sum  of  two  or  more  numbers  is  called 
Addition. 

The  sign  of  addition  (  +  )  is  called  plus.  The  numbers 
between  which  it  s  placed  are  to  be  added.  8  +  6=14  is 
read,  ^'  8  plus  6  equals  14. '^ 

SUBTRACTION. 

55.  1.  The  sum  of  two  numbers  is  14;  one  of  the  num- 
bers is  8.     What  is  the  other  number? 

2.  The  sum  of  two  numbers  is  30;  one  of  the  numbers 
is  5.    What  is  the  other  number? 

3.  Separate  40  into  two  equal  parts,  and  take  out  one  of 
the  parts;  what  remains? 

4.  From  40  take  27. 

5.  What  are  the  two  parts  of  40  in  problem  4? 

6.  Subtract  at  sight : 

40  40  50  60  85  75  60  95  88 
20     10    20     12     15      5    30     12     14 


7.  Read  answers,  subtracting  ones  first: 

126     138     146     137     129     158     169     187 
54346574 


SUBTRACTION. 


47 


8.  42  is  part  of  161.     If  we  subtract  42  from  161,  what 
remains? 

Write  ones  under  ones,  tens  under  tens.    (Place  the  bundles  of 
sticks,  1  hundred,  6  tens,  1  one,  over  the  figures  161.) 

Subtract  ones  first.  2  ones  cannot  be  taken  out  of 
1  one.  Take  1  ten  from  the  tens,  leaving  5  tens. 
(Show  with  the  sticks.) 

The  1  ten  which  we  have  taken  is  equal  to  10  ones, 

which  we  add  to  the  1  one  to  make  11  ones.     2  ones 

from  11    ones  leave  9  ones.      9  is  written  in  ones' 

place  below  the  line.     4  tens  from  5  tens  leave  1  ten, 

which  is  written  in  tens'  place  below  the  line.     No  hundreds 

from  1  hundred  leave  1  hundred,  which  is  written  in  hundreds' 

place  below  the  line. 

119  is  the  part  of  161  which  we  wished  to  find. 
The  two  parts,  42  and  119,  make  what  number  ? 


5     10 

1^1 

4   2 

1    1   9 


5Q.  Subtract: 


EXERCISE. 


(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8) 

171  281  261  252  263  361  260  392 

32   42  34  26  35  28  44  58 

(9)  (10)  (11)  (12)  (13)  (14)  (15)  (16) 

391  282  271  390  471  392  282  373 

54   68  69  72  54  75  67  58 


(17)  (18)  (19)  (20)  (21)  (22)  (23)  (24) 

184  153  174  183  168  173  163  177 

45  35  146  156  59  49  138  148 

(25)  (26)  (27)  (28)  (29)  (30)  (31)  (32) 

340  265  292  290  156  182  280  180 

123  48  147  137  49  55  168  146 


48  SUBTRACTION. 

(33)  (34)  (35)     (36)      (37)      (38)  (39)  (40) 

291  294  162  161  165  261  183  190 

44  58  136  138   59   48  157  129 


(41)   (42)   (43)   (44)   (45)   (46)   (47)   (48) 

290  192  191  187  281  191  271  288 
74   89  168  158   67   69  136  169 


(49)   (50)   (51)   (52)  (53)   (54)  (55)  (56) 

294  390  295  365  293  372  281  390 
69   85  147  148  175  148  167  178 


(57)   (58)  (59)   (60)  (61)   (62)   (63)  (64) 

204  312  315  305  206  304  305  306 
141  191  184  144  156  142  143  164 


(65)  (66)   (67)   (68)   (69)   (70)   (71)   (72) 

300    216    321     222     311     214    304    301 

85      97      84      74      94      65      68     192 

Note. — Just  as  soon  as  possible  have  tlie  pupils  subtract  with- 
out rewriting  the  minuend. 

5*7.  Taking  a  part  of  a  number  out  of  it,  to  find  the 
remainder,  is  called  Subtraction. 

The  number  to  be  diminished  by  taking  one  of  the  parts 
is  called  the  Minuend. 

The  part  taken  out  of  the  minuend  is  called  the  Subtra- 
hend ;  the  part  left  is  called  the  Remainder. 

The  sign  of  subtraction  (  — )  is  called  minus  or  less. 
14—6  =  8  is  read,  ''14  minus  6  equals  8'^;  it  means  that  14 
diminished  by  6  equals  8. 


INCH,  FOOT  AND   YARD.  49 

INCH,  FOOT   AND    YARD. 

One  Inch, 


58.  What  is  the  length  of  the  first  Hne?     Of  the  second? 
The  length  of  the  first  line  is  what  part  of  the  length  of 

the  second? 

The  second  line  is  what  part  of  the  third? 

Cut  a  piece  of  paper  12  inches  long  and  1  inch  wide. 
Draw  a  line  12  inches  long. 

12  inches  make  a  measure  that  is  called  one . 

How  many  six-inch  sticks  of  candy  can  you  cut  from  a 
stick  12  inches  long?     How  many  3-inch  sticks? 

3  inches  are  what  part  of  a  foot? 

How  many  4-inch  lead-pencils  can  be  made  from  a  piece 
of  lead  12  inches  long? 

4  inches  are  what  part  of  a  foot?     8  inches?     One  inch? 
How  many  feet  are  there  in  fifteen  inches?     In  eighteen? 

59.  Draw  a  line  3  feet  long.     Three  feet  make  one  yard. 
Mention  some  things  that  are  sold  by  the  yard. 

How  many  inches  are  there  in  one  yard?  1  foot  is  what 
part  of  a  yard? 

J  a  yard  is  how  many  inches?     How  many  feet? 
i  of  a  yard  is  how  many  inches?     |  of  a  yard? 
12  inches  are  what  part  of  a  yard?    4J  inches? 


50  INCH,  FOOT  AND   YARD. 

Ella  has  a  yard  of  silk  with  which  to  dress  4  dolls  for  the 
fair.  What  part  of  the  silk  will  she  use  for  each  dress,  if  she 
divides  it  equally?    How  many  inches  for  each? 

If  a  yard  of  ribbon  is  divided  for  badges  equally  among 
6  boys,  what  will  be  the  length  of  each  piece? 

In  2  yards  there  are  how  many  feet?  In  3  yards?  How 
many  half  yards  in  2  yards?    How  many  in  3  yards? 

60.  How  many  feet  tall  are  you?  What  is  the  height  of 
the  teacher's  table  from  the  floor?  (Estimate  first,  and 
then  measure.)     What  is  the  length  of  the  table? 

How  far  is  it  from  the  top  of  your  desk  to  the  floor? 
What  is  the  height  of  the  transom  from  the  floor?  Width 
of  window-sash?  Height  of  the  clock  from  the  floor? 
Length,  in  feet,  of  front  blackboard?  Length  of  room? 
Width  of  room? 

Tie  a  knot  for  every  foot  in  a  piece  of  twine  6  feet  long. 
Tie  a  double  knot  for  every  yard. 

Estimate  length,  width,  and  height  of  things  outside  of 
the  schoolroom,  and  then  measure:  height  of  a  barrel;  of 
a  common  wooden  bucket;  length  of  an  ear  of  corn. 

12  inches  (in.)  =  1  foot  (ft.). 
3  feet  =1  yard  (yd.). 

MISCELLANEOUS   PROBLEMS. 

61.  1.  At  10  cents  each,  how  many  pineapples  can  you 
buy  for  30  cents? 

2.  Mary  wishes  to  plant  some  pinks  in  a  triangular  garden 
bed.  How  many  plants  will  she  use,  if  she  plants  10  on 
each  of  the  3  sides?     (Picture.) 


MISCELLANEOUS  PROBLEMS.  51 

3.  How  many  5-cent  pieces  make  30  cents? 

4.  A  church  is  Hghted  by  8  lamps  of  4  burners  each. 
How  many  burners  are  there  in  all? 

5.  George  planted  some  hyacinth  bulbs  in  6  boxes, 
planting  4  bulbs  in  each  box.  How  many  did  he  plant  in 
all? 

6.  A  boy  walks  10  squares  in  30  minutes.  At  that  rate, 
how  long  is  he  in  walking  one  square? 

7.  I  bought  4  verbenas  for  32  cents.  What  did  each 
plant  cost,  if  they  are  of  equal  value? 

8.  Ella  found  4  eggs  each  day  for  a  week;  how  many  did 
she  find? 

9.  How  many  petals  have  8  violets,  if  each  flower  has  5 
petals? 

10.  John  worked  four  weeks.  How  many  days  did  he 
work? 

11.  How  much  money  did  John  earn  if  he  earned  a  dollar 
each  working  day? 

12.  Eleanor  had  3  dimes;  she  spent  6  cents  for  a  pencil. 
How  much  money  had  she  left? 

13.  27  feet  is  three  times  the  length  of  a  ladder;  what  is 
its  length? 

14.  Mary  made  25  sponge-cakes;  she  divided  them 
equally  among  5  brothers  and  sisters;  how  many  did  each 
receive? 

15.  Divide  30  crackers  equally  among  5  boys. 

16.  At  12^  cents  a  can,  what  will  2  cans  of  corn  cost? 

17.  Some  children  were  gathering  goldenrod.  They 
found  that  they  had  gathered  in  all  24  branches.  They 
divided  them  equally  and  each  had  8  branches.  How 
many  children  were  there? 


52  MISCELLANEOUS  PROBLEMS. 

18.  I  wish  to  put  36  quarts  of  milk  into  cans  holding  4 
quarts  each;  how  many  cans  will  be  needed? 

19.  Divide  32  quarts  of  milk  equally  among  4  customers; 
how  many  quarts  will  each  receive? 

20.  48  pounds  of  honey  were  packed  in  4  jars  of  equal 
size ;  how  many  pounds  were  in  each  jar? 

21.  I  bought  some  muslin  for  25  cents  and  had  25  cents 
left;  how  much  money  had  I  at  first? 

22.  John  bought  a  pair  of  skates  for  75  cents  and  sold 
them  for  50  cents.     Did  he  gain  or  lose?    How  much? 

23.  Edgar  sold  a  knife  for  30  cents;  this  is  5  cents  less 
than  he  paid  for  it.     How  much  did  he  pay  for  the  knife? 

24.  A  peck  of  apples  costs  30  cents;  I  must  borrow  5 
cents  in  order  to  pay  for  them;  how  much  money  have  I? 

25.  At  a  picnic  44  cups  of  lemonade  were  passed  to  4 
rows  of  children;  how  many  cups  were  passed  to  each  row? 

26.  How  long  will  48  pounds  of  butter  last,  if  used  at  the 
rate  of  4  pounds  a  week? 

27.  If  you  have  40  pansies  tied  in  bunches  of  10  each, 
how  many  bunches  have  you? 

28.  A  family  used  32  bushels  of  apples  in  8  months;  at 
that  rate,  how  many  bushels  were  used  in  one  month? 

29.  If  36  tuberoses  are  planted  in  4  equal  rows,  how 
many  are  there  in  each  row? 

30.  48  quarts  of  ice-cream  are  how  many  gallons? 

31.  If  Frank  and  James  each  can  mow  the  lawn  in  2 
hours,  in  how  many  hours  can  Frank  and  James  together 
do  the  same  work?  (Will  it  take  a  longer  or  a  shorter  time?) 

32.  Grace  hemmed  six  aprons  in  4  hours;  in  how  many 
hours  can  Grace  and  Mabel  together  do  the  work,  if  Mabel 
works  as  fast  as  Grace? 


MEASURING   TIME.  53 

33.  On  a  journey  of  two  days,  I  traveled  28  miles  the 
first  day  and  67  miles  the  second  day;  how  many  miles 
did  I  travel? 

34.  A  man  earns  125  dollars  in  one  month  and  spends  18 
dollars  for  rent  and  30  dollars  for  groceries;  how  much 
money  has  he  left? 

35.  Edna  gathered  30  pinks,  42  roses  and  24  violets;  how 
many  flowers  did  she  gather? 

36.  Mabel  spent  25  cents  for  some  pencils,  15  cents  for 
paper,  and  40  cents  for  a  book;  how  many  cents  did  she 
spend? 

37.  Emma  spent  5  cents  for  a  pencil  and  had  42  cents 
left;  how  much  money  had  she  at  first? 

38.  I  bought  ^  a  yard  of  velvet  and  found  that  I  needed 
^  of  a  yard  more;  how  much  should  I  have  bought  at  first? 

39.  After  using  |  a  yard  of  ribbon,  I  had  IJ  yards  left; 
how  many  yards  had  I  at  first? 

IIEASURING    TIME. 


62.  Are  there  any  other  ways  of  measuring  time  than  by 
the  clock  and  the  hour-glass?  Have  you  ever  seen  a 
sun-dial? 


54  MEASURING  TIME. 

How  many  minutes  is  the  long  hand  in  passing  from  one 
figure  to  another? 

The  space  between  the  figures  is  divided  into  five  equal 
parts.  The  long  hand  is  a  minute  in  passing  over  one  of 
these  smallest  spaces.  See  how  many  times  you  can  walk 
across  the  floor  in  a  minute.  Sit  still  and  watch  the  clock  a 
minute;  notice  how  much  space  the  long  hand  has  passed 
over. 

Is  any  smaller  portion  of  time  than  a  minute  measured  by 
the  clock?  Some  clocks  tick  60  times  in  a  minute.  Sixty 
seconds  make  a  minute. 

30  seconds  are  what  part  of  a  minute? 

63.  How  long  does  it  take  the  minute  hand  to  move  en- 
tirely round  the  face  of  the  clock?  Count  the  small  spaces 
on  the  face  of  the  clock.     Sixty  minutes  make  an  hour. 

How  many  minutes  are  there  in  2  hours?  5  minutes  are 
what  part  of  an  hour? 

What  time  is  it  by  the  clock  on  page  53?  If  the  long 
hand  were  moved  forward  to  the  figure  1,  what  time  would 
the  clock  show? 

Where  will  the  short  hand  of  the  clock  point  when  the 
minute  hand  points  to  6?  Draw  a  picture  of  the  clock. 
What  time  does  it  show? 

How  many  hours  are  there  from  6  in  the  morning  until 
noon?  How  many  hours  from  noon  until  midnight  ? 
Twenty-four  hours  make  a  day, 

64.  How  many  days  make  a  week?  How  many  weeks 
make  a  month?    Name  the  months  in  order.     Name  those 


MULTIPLICATION  AND  DIVISION.  55 

which  have  30  days.     How  many  days  are  there  in  Feb- 
ruary? 

60  seconds  (sec.)  =  l  minute  (min.). 
60  minutes  =1  hour  (h.). 

24  hours  =1  day  (d.). 

7  days  =lweek(w.). 

4  weeks  =  1  month  (m.). 

12  months  1 


365  days 


I        =lyear(yr.). 


MULTIPLICATION   AND    DIVISION. 

65.  Copy  and  learn: 

5X5  =  25  7X5  =  35  9X5  =  45  11X5-55 

6X5  =  30  8X5  =  40  10X5  =  50  12X5  =  60 

Write  the  table  with  the  5's  first. 

Recite  the  division  table  from  the  multiplication  table. 

Thus,25-5  =  5        30^6  =  5,  etc. 
30^5  =  6 

EXERCISE. 

66,  1.  At  5  dollars  a  pair,  what  will  5  pairs  of  shoes  cost? 

2.  If  a  family  uses  5  pounds  of  butter  in  one  week,  in  how 
many  weeks  will  30  pounds  be  used? 

3.  At  5  cents  a  pound,  how  many  pounds  of  sugar  can  be 
bought  for  45  cents? 

4.  40  loaves  of  bread  will  last  a  camping  party  how  many 
days,  if  they  use  5  loaves  a  day? 

5.  At  5  cents  a  spool,  how  many  spools  of  thread  can  be 
bought  for  60  cents? 


56  MULTIPLICATION  AND  DIVISION. 

6.  If  a  yard  of  cloth  costs  5  dollars,  what  will  7  yards 
cost? 

7.  If  a  man  earns  5  dollars  a  day,  how  many  dollars  does 
he  earn  in  a  week,  counting  6  working  days? 

8.  Mabel  gathered  35  roses  which  she  divided  among  her 
friends,  giving  5  roses  to  each;  among  how  many  friends  did 
she  divide  them? 

9.  At  5  cents  a  paper,  what  will  a  dozen  papers  of  needles 
cost? 

10.  If  it  takes  5  yards  of  cloth  to  make  a  suit  of  clothes, 
how  many  suits  can  be  made  from  55  yards? 

11.  Make  problems  for : 


9X5=45 

5)45 

5)35 

8X5=40 

7X5=35 

9 

7 

6X5  =  30 

12X5=60 

5)55 

5)50 

5X6=30 

5X8=40 

11 

5 

11X5=55 

Note. — Do  this  in  class. 

67.  Copy  and  learn: 

6X6  =  36        8X6  =  48        10x6  =  60        12X6=72 
7X6  =  42        9X6  =  54        11X6  =  66 

Write  the  table  with  the  6^s  first. 

Recite  the  division  table  from  the  multiplication  table. 

EXERCISE. 

68.  1.  How  many  yards  of  fringe  will  be  needed  for  7 
rugs,  if  6  yards  are  used  for  one  rug? 

2.  When  melons  are  selling  for  12  cents  each,  what  will  6 
cost? 


FINDING  ONE  OF  THE  EQUAL  PARTS  OF  A  NUMBER.  57 

3.  At  6  dollars  each,  how  many  flags  can  be  bought  for  48 
dollars? 

4.  If  I  use  6  small  flags  for  decorating  one  window,  how 
many  shall  I  need  for  9  windows? 

5.  In  how  many  months  can  I  pay  for  a  sewing  machine 
which  costs  60  dollars,  if  I  pay  6  dollars  a  month? 

6.  How  many  inches  are  there  in  a  yard?    How  many 
badges  6  inches  long  can  be  cut  from  one  yard  of  ribbon? 

7.  A  merchant  sold  a  dozen  silk  umbrellas  at  6  dollars 
each;  how  much  money  did  he  receive  in  payment? 

8.  At  6  dollars  a  dozen,  what  will  5  dozen  spoons  cost? 

9.  I  received  66  dollars  for  11  barrels  of  apples;  how 
much  is  that  a  barrel? 

10.  If  6  gallons  of  oil  are  used  in  a  month,  how  long  will 
48  gallons  last? 

11.  Make  problems  for: 


9X6  = 

6)48 

6)36 

11X6= 

8 

6 

.2X6  = 

6)54 

6)^ 

7X6= 

9 

12 

Note. — Do  this  in  class. 

Finding  One  of  the  Equal  Parts  of  a  Number. 

EXERCISE. 

69.  1.  If  6  yards  of  cloth  cost  30  dollars,  what  is  the 
cost  of  one  yard? 

2.  Frank  walks  35  miles  in  5  days;  at  that  rate  how 
many  miles  does  he  walk  in  one  day? 


58  FINDING  ONE  OF  THE  EQUAL  PARTS  OF  A  NUMBER. 

3.  42  pounds  of  butter  are  packed  in  6  jars  of  equal  size; 
how  many  pounds  are  put  in  each  jar? 

4.  I  paid  60  cents  for  a  dozen  oranges;  at  that  rate,  what 
is  the  cost  of  one  orange? 

5.  George  planted  45  tulip  bulbs  in  5  equal  rows;  how 
many  did  he  plant  n  one  row? 

6.  A  man  earned  72  dollars  in  6  weeks;  at  that  rate  how 
much  does  he  earn  in  one  week? 

7.  Six  children  were  gathering  shells;  they  found  that 
they  had  gathered  54  in  all.  If  they  divided  them  equally, 
how  many  did  each  child  receive? 

8.  A  boy  walks  9  squares  in  27  minutes;  how  long  is  he  in 
walking  one  square? 

9.  If  9  pounds  of  rice  cost  72  cents,  what  is  the  cost  of  one 
pound? 

10.  A  gardener  takes  4  dozen  plants  to  market  and  sells 
only  one-sixth  of  them;  how  many  plants  does  he  sell? 

11.  Make  problems  for: 

i  of  60=10  5)30  apples  60h-6  =  10 

6  apples 

i  of  40  =  8  6)72  cents  42-6  =  7 

12  cents 

i  of  54  =  9  5)60yards  72-12  =  6 


12  yards 


Note. — Do  this  in  class. 


70.  Copy  and  complete : 

5^5  =  1 

8-h5  = 

11^5  = 

6  -^5=  1,  and  1  remaining 

9-5  = 

12^5  = 

7  -r5  =  1,  and  2  remaining 

10-^5  = 

13-^5  = 

REVIEW  OF  MULTIPLICA TION,  59 


14^5  = 

21^5= 

28^5  = 

15^5  = 

22 --5  = 

29^5  = 

16-4-5= 

23^5  = 

30h-5  = 

17-^5= 

24h-5  = 

31^5= 

18^5  = 

25^5  = 

32^5= 

19h-5  = 

26^5  = 

33^5  = 

20^5  = 

27-^5  = 

34^5= 
35h-5= 

Divide  all  numbers  from  6  to  36,  by  6. 

71.  REVIEW. 

1X2=  2  1X3=  3                  1X4=  4 

2X2=  4  2X3=  6                  2X4=  8 

3X2=  6  3X3=  9                  3X4  =  12 

4X2=  8  4X3  =  12                  4X4  =  16 

5X2  =  10  5X3  =  15                  5X4=20 

6X2  =  12  6X3  =  18                  6X4  =  24 

7X2  =  14  7X3  =  21                  7X4  =  28 

8X2  =  16  8X3  =  24                 8X4  =  32 

9X2  =  18  9X3  =  27                  9X4  =  36 

10X2  =  20  10X3  =  30                10x4  =  40 

11X2  =  22  11X3  =  33                11X4  =  44 

12X2  =  24  12X3  =  36                12x4  =  48 

1X5=  5  7X5  =  35 

2X5  =  10  8X5  =  40 

3X5  =  15  9X5  =  45 

4X5  =  20  10X5  =  50 

5X5  =  25  11X5  =  55 

6X5  =  30  12X5  =  60 


60  ADDITION  TABLE. 

1X6=  6  7X6  =  42 

2X6  =  12  8X6  =  48 

3X6  =  18  9X6  =  54 

4X6  =  24  10X6  =  60 

5X6  =  30  11X6  =  66 

6X6  =  36  12X6  =  72 

Without  rewriting,  read  these  with  2,  3  4,  5  and  6  first. 

72.  ADDITION    TABLE. 

1    2    32    43    543 
1    1    12    12    12  3 


654    7654    8765 
123    1234    1234 

98765   9876 
12345    2345 

9876   987   987 
3456   456   567 

9  8   9  8   9   9 
6  7    7  8   8   9 


Note. — The  45  sums  given  above  must  be  learned  as  the  basis 
for  accuracy  and  rapidity  in  addition. 

73.  SUBTRACTION    TABLE. 

2        33        444        5555 
1        12        123        1234 


SUBTRACTION   TABLE.  61 

66666   777777 
12345    123456 


9  9 
1  2 

9  9  9  9 
3  4  5  6 

9  9 

7  8 

10  10  10 
1   2   3 

10  10  10 
4   5   6 

10  10 

7   8 

10 
9 

11   11   11   11   11   11   11   11 

23456789 


12 

12 

12 

12 

12 

12 

12 

3 

4 

5 

6 

7 

8 

9 

13     13     13     13     13     13  14     14     14     14     14 


4   5   6   7 

8   < 

) 

5 

6   7   8   9 

15  15  15  15 

6   7   8   9 

16 

7 

16 

8 

16 
9 

17  17    18 
8   9     9 

Note. — These  74  primaiy  facts  of  subtraction  should  be 
thoroughly  learned.  These  tables  should  be  frequently  reviewed. 
They  should  be  placed  on  the  board  or  on  a  chart  so  that  they 
may  be  readily  used. 


CHAPTER  IV. 
READING  AND  WRITING   NUMBERS  :   THOUSANDS. 

74.  You  have  learned  that  the  number  one  thousand  is 
expressed  by  writing  the  figure  1  to  the  left  of  hundreds' 
place. 

Read  the  following  numbers : 

1,500        1,230        1,400        1,670        1,873        1,999 
1,220        1,864        1,748        1,976        1,449        1,650 

The  period  of  ones  is  separated  from  the  thousands  by  a 
comma. 

Write  in  figures:  two  thousand,  three  thousand,  five 
thousand,  eight  thousand,  nine  thousand. 

Read  the  following  numbers: 

3,000  7,000  6,350 

3,200  5,102  8,008 

4,340  2,501  8,108 

8,650  7,206  0,888 

9,241  7,777  5,230 

The  greatest  number  that  can  be  expressed  by  four  figures 
is  9,999. 
Write  in  figures: 

Three  thousand  seven  hundred  fifty. 

Eight  thousand  two  hundred  two. 

One  thousand  eleven;  one  thousand  one. 

Five  thousand  five;  five  thousand  fifty. 

Four  thousand  thirty-five;  four  thousand  five. 


4,500 

9,400 

1,111 

0,444 

1,001 

2,020 

1,100 

4,009 

1,004 

9,999 

READING  AND  WRITING  NUMBERS:  THOUSANDS.     63 
Express  in  figures  numbers  composed  of : 

0  thousands  6  hundreds  7  tens  and  4  ones. 


3 

l( 

3 

U 

3 

ii 

li 

3 

li 

9 

iC 

8 

iC 

5 

(C 

(C 

6 

11 

8 

a 

0 

u 

0 

{( 

a 

7 

cc 

5 

(( 

9 

IC 

9 

(C 

C( 

0 

IC 

15.  Write  one  thousand  in  figures.  In  what  place  does 
the  figure  1  stand?  If  we  wish  to  express  a  number  ten 
times  as  great  as  1,000,  how  shall  we  represent  it?  One  ten- 
thousand  is  ten  times  as  great  as  one  thousand.  We  ex- 
press the  1  ten-thousand  by  writing  the  figure  1  to  the  left 
of  thousands,  in  ten-thousands'  place;  thus,  10,000. 

Note. — A  box  of  small  toothpicks  may  be  used  in  bundles  of 
tens,  hundreds,  and  thousands,  to  show  the  ten-thousand. 

1.  Write  2  ten-thousands.  2  ten-thousands  are  how 
many  ones? 

2.  Write  3  ten-thousands  and  read  the  number  in  two 
ways.     (How  many  thousands?     How  many  ones?) 

3.  Read  the  following  numbers: 


30,000 

25,400 

15,021 

10,010 

50,000 

36,303 

21,048 

11,001 

90,000 

47,350 

16,743 

15,005 

41,000 

54,707 

28,096 

15,015 

65,000 

90,900 

11,110 

99,999 

4.  How  many  ones  are  there  in  each  of  the  last  five  num- 
bers? 


64 


ROMAN  NOTATION. 


5.  Write  the  following  in  figures: 

27  thousand  600  ones.  30  thousand  500  ones. 

70  thousand  350  ones.  60  thousand    70  ones. 

6  thousand    70  ones.  95  thousand  200  ones. 

80  thousand      8  ones.  8  thousand      8  ones. 


_     6.  Write  in  figures: 

Seventeen  thousand  seven. 

Twenty  thousand  two. 

Eighty  thousand  eighty-one. 

Twelve  thousand  twenty- 
one. 

Eleven  thousand  one. 

Eleven  thousand  one  hun- 
dred ten. 


Seventeen  thousand  seven- 
teen. 

Ninety  thousand  nine. 

Twelve  thousand  twelve. 

Fifty-six  thousand  one  hun- 
dred fifty-six. 

Ten  thousand  ten. 

Eleven  thousand  eleven. 


•76, 

30       40 
XXX      XL 


ROMAN   NOTATION. 

50        60        70        80        90        100 
L  LX     LXX  LXXX    XC  C 


When  a  letter  is  repeated,  its  value  is  repeated. 

When  a  letter  is  placed  after  one  of  greater  value,  its  value  is 
added;  when  placed  before,  its  value  is  subtracted  from  the 
greater. 

Express  the  following  numbers  by  figures: 


XXXIX 

LIX 

XC 

XCIX 

XLIX 

LXV 

XCI 

XCVIII 

XLVIII 

LXX 

LXXXIX 

LXXIX 

XIX 

XLIV 

XCVIII 

XLIV 

XXIX 

LXXX 

LXXXVIII 

LXVI 

M  ULTI  PLICA  TION.  65 

Express  the  following  numbers  by  letters : 


45 

94 

42 

49 

51 

87 

58 

59 

68 

61 

75 

99 

73 

49 

95 

83 

MULTIPLICATION. 

YTo  Two  times  24  cents  are  how  many  cents? 
2  times  $80=? 
2  times  396=? 

Two  times  6  ones  are  12  ones.     12  ones  equal  1  ten         396 
and  2  ones.     Write  the  2  ones  in  ones'  place.  2 

2  times  9  tens  are  18  tens  ;  adding  1  ten  we  have         

19  tens,  equal  to  1  hundred  and  9  tens.     Write  9  tens  792 

in  tens'  place. 

2  times  3  hundreds  are  six  hundreds;  adding"  one  hundred  we 
have  7  hundreds,  which  we  write  in  hundreds'  place. 

2  times  396  equal  792. 

Find  the  same  result  by  addition,  and  notice  the  number  of 
ones  added ;  the  number  of  tens,  etc. 

396  is  called  the  Multiplicand;  it  is  the  number  to  be 
multiplied. 

2  is  called  the  Multiplier;  it  is  the  number  which  shows 
how  many  times  the  multiplicand  is  taken. 

792  is  called  the  Product;  it  is  the  result  obtained  by 
multiplying. 

The  multiplicand  and  the  multiplier  are  called  Factors 
(makers)  of  the  product. 

The  sign  of  multiplication  is  X;  read  "  multiplied  by.^' 
396X2  =  792  is  read,  ''  396  multiplied  by  2  equals  792/' 


66  MULTIPLICATION. 

EXERCISE. 

78.  1.  If  a  man  travels  96  miles  in  a  day,  how  far,  at 
that  rate,  will  he  travel  in  2  days? 

96  miles,  distance  traveled  in  1  day. 
2 
192  miles,  distance  traveled  in  2  days. 

2.  At  $2  a  box,  what  will  87  boxes  of  lemons  cost? 

$2,  cost  of  1  box. 
87 
$174,  cost  of  87  boxes  of  lemons. 
87  times  $2  =  $174. 
Multiply  87  by  2,  and  call  the  result  dollars. 

3.  What  will  126  pairs  of  shoes  cost,  at  $2  a  pair? 

4.  If  a  train  runs  328  miles  in  a  day,  how  far  will  it  run 
in  2  days? 

5.  How  many  feet  have  837  men? 

6.  How  many  eyes  have  918  men? 

7.  At  $2  a  yard,  what  will  be  the  cost  of  528  yards  of 
cloth? 

8.  What  will  929  barrels  of  apples  cost,  at  $2  a  barrel? 


Multiply: 

(9)     (10) 

378   856 

(11) 
504 

(12) 

978 

(13)     (14) 

709   768 

(15) 

980 

2     2 

2 

2 

2     2 

2 

(16)     (17) 

309    2023 

(18) 

986 

(19)      (20) 

4507    4659 

(21) 

4709 

2      2 

2 

2      2 

2 

DIVISION.  67 

22.  468  multiplied  by  2=  ?     25.  349  multiplied  by  2  =  ? 

23.  763  ''  2=?     26.  786  "  2=? 

24.  849  "  2=?     27.  605  "  2=? 


DIVISION. 

79.  How  many  times  can  2  cents  be  taken  out  of  50 
cents?  How  many  times  out  of  80  cents?  Out  of  90 
cents? 

How  many  2's  can  be  taken  out  of  9  tens  8  ones? 

Show  with  the  counters  that  45  twos  can  be  taken  out  of  9  tens, 
or  90  ones,  and  that  4  twos  can  be  taken  out  of  8  ones.  49  twos 
can  be  taken  out  of  9  tens  8  ones. 

Show  that  9  tens  (or  90)  hold  2  ones  4  tens  (or  40)  times,  with 
1  ten  remaining.  The  1  ten  is  equal  to  10  ones.  10  ones  and  8 
ones  are  18  ones.     18  ones  hold  2  ones  9  times. 

How  many  2's  can  be  taken  out  of  972? 

2  is  contained  in  9  hundred  4  hundred  times,  with  2)972 
1  hundred  remaining  undivided,  which  is  equal  to  10  AQa 

tens.     10  tens  and  7  tens  are  17  tens.     2  is  contained  in 
17  tens  8  tens  times,  with  1  ten  remaining,  which  is  equal  to  10 
ones.     10  ones  and  2  ones  are  12  ones.     2  is  contained  in  12  ones 
6  times.     2  can  be  taken  out  of  972  486  times,  or  486  twos  can  be 
taken  out  of  972. 

How  many  $2  are  there  in  $972? 

At  $2  a  barrel,  how  many  barrels  of  potatoes  can  be 
bought  for  $972? 

$2)  $972 

486,  number  of  2-doIlars  is  $972. 
486  barrels  of  potatoes,  at  $2  a  barrel,  can  be  bought  for  $972. 


68  DIVISION, 

972  is  called  the  Dividend. 
2  is  called  the  Divisor. 

A  divisor  is  called  an  Exact  Divisor  when  it  is  contained 
in  the  dividend  without  a  remainder. 
Divide  73  by  2.  2)_73 

36—1 
1  is  the  remainder  and  the  division  is  not  exact. 

486  is  called  the  Quotient ;  it  is  the  result  of  the  division. 
The  divisor  and  quotient  are  Factors  of  the  dividend. 
The  product  of  the  divisor  and  the  quotient,  plus  the 
remainder,  is  equal  to  the  dividend. 

In  the  problem  above,  2  is  divisor,  36  quotient,  and  1  re- 
mainder.    36  X  2  =  72 ;  72  + 1  =  73.     73  is  the  dividend. 

Division  is  expressed  in  three  ways.  Each  of  the  ex- 
pressions, 24  -2  =  12,  V  =  12,  and  2)24,  is  read,  ''24  divided 
by  2  equals  \2r  12 

80.  Divide  by  2: 

1.  7398     4.  8604     7.  7176     10.  2015 

2.  8249     5.  7170     8.  1257     11.  4819 

3.  9781     6.  9410     9.  6729     12.  9197 

EXERCISE. 

81.  1.  One  half  of  90  cents  is  how  many  cents? 

2.  Divide  9  dimes  equally  between  2  boys;  how  many 
dimes  will  each  receive? 

3.  Find  ^  of  9  tens  8  ones. 

i  of  9  tens  is  4  tens,  with  1  ten  remaining,  which  is  equal  to  ten 
ones.  Ten  ones  and  8  ones  are  18  ones.  \  of  18  ones  is  9  ones. 
One-half  of  9  tens  8  ones  is  49  ones.     (Show  by  counters.) 


MULTIPLYING  AND  DIVIDING  BY  3.  69 

4.  A  man  divided  $972  equally  between  his  two  children; 
how  much  money  did  each  receive? 

2 )  $972,  money  to  be  divided. 

I486,  money  each  child  received. 

Find  J  of : 

5.9875     7.9347     9.3098     11.  $8101      13.  7003  bushels. 
6.  6001     8.  7190    10.  5729     12.  $7900     14.  5045  pecks. 

EXERCISE. 

82.  1.  If  a  man  travels  286  miles  in  2  days,  at  that 
rate  how  far  will  he  travel  in  one  day? 

2.  A  clock  strikes  312  times  in  2  days;  how  many  times 
does  it  strike  in  1  day? 

3.  How  many  times  must  we  take  the  number  2  to  make 
652? 

4.  If  a  man  earns  $2  a  day,  how  long  will  it  take  him  to 
earn  $550? 

5.  A  bookseller  paid  $114  for  photograph  albums  at  $2 
each;  how  many  did  he  buy? 

6.  A  gardener  had  750  strawberry  plants,  and  sold  J  of 
them;  how  many  did  he  sell? 

7.  What  number  multiplied  by  2  will  produce  1680? 

MULTIPLYING  AND  DIVIDING  BY  3. 

83.  Find  the  products  of: 

1.  3086X3     4.    3006X3  7.    3009X3        10.   4123X3 

2.  3097X3     5.    3246X3  8.    2549X3        11.   2867x3 

3.  2786X3     6.    3269x3  9.    3369X3        12.    3009X3 
13.  3  multiplied  by  2738=?  14,  3  multiplied  by  3108=? 


70       MULTIPLYING  AND  DIVIDING  BY  4,  5,  AND  6. 

Find  the  quotients  of : 

15.  3687^3     17.    7891 -^3     19.   2501^3      21.   9108^3 

16.  3456-7-3     18.   5476-^3    20.   7057^3      22.   8310-^3 

EXERCISE. 

84.  1.  How  many  3-cents  are  there  in  3564  cents? 

2.  How  many  yards  are  there  in  a  coil  of  wire  which 
contains  2500  feet? 

3.  What  will  687  yards  of  cloth  cost,  at  $3  a  yard? 

4.  A  man  saved  $3  a  week;  in  how  many  weeks,  at  that 
rate,  will  he  save  $450? 

5.  If  a  steamer  can  run  278  miles  a  day,  how  far  can  it 
run  in  3  days? 

6.  $241  is  i  of  my  money;  how  much  money  have  I? 

7.  Three  times  $395  is  the  price  of  a  lot;  what  is  the 
value  of  the  lot? 

8.  Find  dividends: 

3)  3)  3)  3) 


241  335  35J  680 

9.  How  is  the  dividend  found,  when  divisor  and  quo- 
tient are  given?    What  are  the  factors  of  the  dividend? 


MULTIPLYING  AND  DIVIDING   BY  4,  5,   AND    6. 

85.  Find  products  of: 

1.  856X4  3.    968X4        5.    2079x4        7.    1976X4 

2.  2798X4  4.    989X4        6.    2098X4        8.    1678x4 


MULTIPLYING  AND  DIVIDING  BY  4,  5,  AND  6.       71 


Find  quotients  of: 

9.   6789  -^4 

10.  2135  -f-4 

11.  14009-^4 

12.  15203  H-4 

86.  Find  products  of: 

1.  1856X5       3.    2765X5 

2.  2708X5       4.    3769X5 

Divide  by  5: 

9.    19290  12.  18605 

10.  94806  13.  43441 

11.  31433  14.  38024 

87.  Multiply  by  6: 

1.  9874      4.  5907 

2.  3009      5.  8679 

3.  0068      6.  1948 

Divide  by  6: 

13.  32430  16.  44445 

14.  34850  17.  46847 

15.  37838  18.  49250 


13.  31033  -f-4 

14.  67890  -^4 

15.  34035  -4 

16.  39393  ^4 


5.  3579X5 

6.  1978X5 

15.  46979 

16.  37300 

17.  54306 


7.  7308 

8.  5897 

9.  6087 


19.  56457 

20.  58259 

21.  57456 


7.  1948X5 

8.  1067X5 


18.  47464 

19.  89180 

20.  34744 


10.  9396 

11.  2958 

12.  1769 

22.  17171 

23.  19191 

24.  31433 


88.  CLASS  EXERCISE. 

Note. — Each,  pupil  in  turn  should  multiply  or  divide  one  num- 
ber by  6  and  add  the  number  carried  over,  or  give  the  remainder. 
1.  431024516819278  2.  843765074957 

6  6 


3.  6)468471029872109 


4.  6)23453840196 


72  UNITED  STATES  MONEY. 

UNITED  STATES  MONEY. 

89.  Draw  a  one-cent  piece.  Draw  a  dime.  How  many 
cents  equal  a  dime? 

How  many  cents  make  a  dollar? 

How  many  tens  make  one  hundred?  How  many  dimes 
make  a  dollar?    One  dollar  is  written,  $1. 

10  cents  =  1  dime. 
10  dimes  =  $1. 

Half  a  dollar  is  how  many  cents?  50  is  what  part  of  100? 
60  cents  is  what  part  of  $1? 

25  cents  is  what  part  of  100  cents?  What  part  of  $1? 
What  part  of  50  cents? 

f  of  $1  are  how  many  cents?    ^  of  $1  is  how  many  cents? 

i  of  $1  is  how  many  dimes?  i  of  $1  is  how  many  dimes? 
Half  a  dime  is  how  many  cents? 

If  I  spend  I  of  $1,  how  many  fourths  of  $1  shall  I  have 
left?    How  many  cents? 

Find  with  counters  (buttons  or  circular  discs)  100  cents; 
find  5  more  cents  How  many  cents  have  you?  How 
many  dollars  and  cents? 

To  show  that  we  have  one  dollar  and  five  cents,  we  write 
it  in  this  way:  $1.05,  placing  a  period  between  dollars  and 
cents. 

Write  one  dollar  and  three  cents;  one  dollar  and  six 
cents. 

The  cents  are  written  at  the  right  of  the  dollars,  with  a  period 
between  the  dollars  and  cents.  Two  places  are  required  to 
express  cents  when  the  dollar  sign  is  used. 


UNITED  STATES  MONEY,  73 

90.  1.  Begin  with  $1,  and  write  all  the  dollars  and  cents 
up  to  $1.25. 

2.  Write  the  following  in  figures : 

One  dollar  fifty  cents;  one  dollar  and  sixty-nine  cents; 
one  dollar  one  cent;  one  dollar  and  ninety-nine  cents. 

3.  Read  the  following: 

$0.06  $1.02  $1.10  $1.70  $0.03 

$1.00  $1.09  $1.01  $1.71  $1.44 

$1.07  $1.90  $1.75  $1.17  $1.50 

$1.88  $1.17  $0.98  $1.27  $1.80 

$1.11  $1.60  $1.36  $1.05  $1.08 

4.  Write  the  above  numbers  and  add. 

Add  as  in  simple  numbers  and  separate  dollars  from  cents  by  a 
period. 

5.  How  many  cents  are  there  in  $2?    In  $3?    In  $4? 

6.  Write  the  following  in  figures : 

Two  dollars  seven  cents ;  two  dollars  twelve  cents ;  three 
dollars  forty  cents;  four  dollars  ninety  cents;  five  dollars 
nine  cents;  seven  dollars  seven  cents. 

7.  Read  the  following : 

$6.08  $0.01  $5.05  $6.15  $7.71  $20.05 

$9.10  $8.01  $4.01  $6.51  $7.07  $30.50 

$7.05  $9.09  $3.10  $0.05  $10.50  $29.16 

$4.04  $5.50  $6.11  $7.17  $10.05  $40.12 

8.  How  many  cents  are  there  in  two  dollars  ninety-five 
cents? 

9.  How  many  dollars  in  six  hundred  fifty  cents? 
10.  How  many  hundreds  in  seven  hundred  ninety? 


74        ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

11.  How  many  50's  in  200?    How  many  50-cent  pieces 
in  $2? 

12.  Put  down  a  dollar  for  eael^  hundred  cents  in  ten 
dollars.     How  many  hundred  cents  make  ten  dollars? 

13.  How  many  cents  make  seven  dollars  seven  cents? 

14.  Find  the  sum  of  $9.06  and  $12.20. 

15.  Find  the  sum  of  $15.25  and  $4.30. 

16.  Subtract: 

$12.00-  $5.00.  $20.00— $6.00. 

$15.50- $12.50.  $9.30— $8.30. 

Subtract  as  in  simple  numbers,  and  separate  dollars  from  cents 
by  a  period. 

ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

91.  Write  ten  numbers  ending  in  4;  add  2  to  each  of 
these  numbers. 

14    24    34    44    54    64    74    84    94     104 
222222222        2 


With  what  figure  does  each  sum  end? 
Make  a  subtraction  table  by  using  the  results  of  addi- 
tion obtained  above  and  subtracting  2  from  each.     Thus: 

16    26    36    46    56    66    76    86    96    106 
JJ       2      2      2       2       2       2       2        2 

With  what  figure  does  each  remainder  end? 

Write  ten  numbers  ending  in  3,  and  add  4  to  each  num- 
ber.    What  is  the  ending  figure? 

Write  the  results  of  additions  obtained  above  and  sub- 
tract 4  from  each  number.     What  is  the  ending  figure? 


ADDITION  AND  SUBTRACTION   BY  ENDINGS.        75 

93.  1  +  8. 

Add,  giving  first  the  ending  figure  of  the  sum,  and  then 
the  whole  sum : 

8    18    28    38    48    58    68    78    88    98 
IJLJJL       IJ.       1       1_1_1 

1     11     21     31     41     51     61     71     81     91 

Write  the  results  of  addition  obtained  above  and  sub- 
tract 1  from  each  number.     Subtract  8  from  each. 
Add,  beginning  at  the  left: 

1,  8,  1,  1,  8,  1,  1,  8,  1,  1,  8,  1,  8,  1,  1,  8. 

8,  1,  1,  8,  1,  1,  1,  8,  1,  1,  8,  1,  8,  1,  1,  1. 

9,  6,  3,  1,  1,  1,  8,  1,  8,  1,  1,  8,  1,  1,  1,  8. 
6,  8,  4,  1,  1,  8,  1,  1,  1,  8,  1,  8,  1,  1,  1,  8. 

93.  1+9. 

Add  9  to  numbers  ending  in  1 : 

1  11  21  31  41  51  61  71  81  91 

Make  a  subtraction  table,  taking  9  from  each  of  the  re- 
sults of  addition  obtained  above. 
Add,  beginning  at  the  left : 

1,   9,   9,    1,    1,   9,    1,   9,    1,   9,  1,  9,  1,  9,  1,   9. 

9,    1,    1,   9,    9,    1,    1,   9,    9,    1,  1,  9,  1,  9,  9,    1. 

8,  8,   4,    1,    9,    1,   9,    8,    1,    1,  9,  1,  9,  1,  9. 

9,  8,   3,   9,    1,    1,    9,    1,   9,    9,  1,  1,  9,  5,  1. 

8,   7,   5,   9,    1,    8,    1,    1,   9,    1,    1,   9,    1,   9,   9,    1. 


76  ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

Add,  beginning  at  the  bottom  of  the  hne : 

(1)      (2)      (3)      (4)      (5)      (6)      (7)      (8)      (9)    (lO)   (11)   (12) 


9      1 

1 

9 

2 

9 

8 

9 

8 

9 

9 

1 

1      9 

1 

1 

8 

1 

1 

1 

1 

1 

1 

9 

9      1 

8 

9 

1 

9 

8 

3 

9 

1 

9 

1 

1      9 

1 

9 

8 

1 

1 

6 

1 

9 

1 

1 

1      1 

8 

1 

1 

1 

9 

9 

1 

9 

1 

5 

8      1 

1 

9 

1 

1 

1 

1 

9 

1 

8 

4 

1      9 

9 

1 

9 

8 

1 

1 

9 

1 

1 

1 

9      9 

1 

1 

1 

1 

8 

9 

1 

9 

9 

9 

1      1 

1 

9 

1 

9 

1 

1 

1 

1 

1 

1 

1      4 

1 

5 

8 

7 

7 

3 

1 

5 

9 

7 

9      8 

9 

9 

1 

4 

5 

7 

3 

7 

6 

6 

9      8 

9 

6 

9 

9 

8 

9 

5 

7 

5 

6 

Copy  and 

1  add: 

(1)  (2)  (3)  (4)  (6)  (6)  (7)  (8)  (9)  (10) 

99  99  99  88  98  19  99  89  99  91 

91  11  11  11  91  91  99  19  11  19 

11  11  11  98  19  11  11  91  99  91 

19  88  19  11  91  18  11  11  11  19 

99  91  81  99  11  89  19  99  11  11 

11  19  90  11  19  10  89  11  91  91 

11  11  18  11  89  91  11  11  98  19 

81  19  11  31  11  19  15  81  14  16 

93  46  99  39  99  94  47  98  68  46 

75  95  61  99  71  67  98  79  98  98 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.  77 

94.  2  +  5  and  2  +  6. 

Add  5  and  6  to  numbers  ending  in  2.     Read  the  ending 
figure  first,  then  the  whole  sum : 

2     12     22     32     42     52     62     72     82     92     102 

2     12     22     32     42     52     62     72     82     92     102 
6      666666666        6 

Make  subtraction  tables  by  using  the  results  of  addition 
and  subtracting  5  from  each.     Subtract  6  from  each. 
Copy  and  add: 

(1)      (2)      (3)      (4)      (5)      (6)      (7)      (8)      (9)     (10) 

15  16  16  81  16  22  15  51  69  66 

62  11  52  11  12  11  61  21  11  22 

21  69  21  16  51  91  21  16  19  11 

19  21  11  62  21  16  16  12  11  91 

11  11  18  21  16  12  12  61  51  16 

81  16  61  11  92  61  81  21  26  12 

11  62  21  14  11  21  11  11  12  61 

15  25  16  27  11  11  12  14  19  29 

65  97  89  57  69  99  68  67  65  97 
97788380997898968683 

95.  2  +  7. 

Add: 

2     12     22     32     42     52     62     72     82    92     102 

7777777777        7 

Make  a  table,  subtracting  7  from  each  of  the  results  of 
addition  above. 


78  ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

Add,  beginning  at  the  left: 

2,   7,    1,   9,    1,   2,    7,    1,  1,   9,   2,    7,  1,  2,   7. 

9,   8,   2,    1,    9,    1,    2,    7,  1,    2,    7,    1,  9,  1,    2. 

6,   6,   5,   2,    1,   2,    6,    1,  1,    2,   5,    2,  1,  2,    7. 

Copy  and  add: 

(1)      (2)     (3)      (4)      (5)  (6)      (7)      (8)  (9)  (10) 

97  87  72  11  67  79  11  71  11  19 

12  12  21  77  21  21  71  27  79  71 

71  11  17  22  17  11  26  12  21  27 

27  61  92  11  72  26  12  71  97  92 

12  26  11  79  21  52  71  27  12  19 

91  12  79  21  19  21  27  12  19  11 

12  71  21  11  91  12  12  91  91  91 

3  22  11  92  17  74  29  18  14  11 

77  98  79  98  77  28  45  77  78  79 

97  89  89  78  85  75  96  84  78  89 


EXERCISE. 


96.  Subtract: 


(1)  (2)  (3)  (4)  (5)  (6) 

4221  5121  7011  3121  6321  4112 
132   223   213   232   332   123 


7.  9131-322=?  13.  2121-312=? 

8.  4011-303=?  14.  4118-223=? 

9.  5210-223=?  15.  5102-213=? 

10.  3101—222=?  16.  6110-123=? 

11.  5119-223=?  17.  8112-213=? 

12.  3122-123=?  18.  7231-322=? 


DRY  MEASURES. 

Subtract : 

(19)        (20)         (21)         (22)         (23)        (24) 

4310  5301  8234  6202  8402  5021 
234   404   344   334   314   334 


79 


25.  5012-  223  =  ?  31.  9139-244=?  37.  9301-3544=? 

26.  4610  -  132  =  ?  32.  81 23  -  334  =  ?  38.  4302  - 1443  =  ? 

27.  7051-  233=?  33.  5210-334=?  39.  6201-  344=? 
28.6311-  233=?  34.9401-424=?  40.9032-  334=? 
29.5012-  213  =  ?  35.5204-325=?  41.6020-2344=? 
30.  6300-1311  =  ?  36.  9103-234=?  42.  8023-3254=? 


CLASS  EXERCISE. 

07.  Note. — Let  each  pupil  subtract  one  number. 

1.  820431290425613      2.  76498364271503 
624153423542134        53726547326174 


3.  87365419854721 
28158274936294 


4.  3746937100 
2587394837 


DRY  MEASURES. 


8 

Pint. 


Quart. 


Peck. 


98.  1,  A  quart  of  berries  is  how  many  pints? 
2.  A  peck  of  beans  is  how  many  quarts? 
Eight  quarts  make  a  peck. 


80  DRY  MEASURES. 

3.  Where  have  you  seen  these  measures  used?  Name 
some  things  which  you  have  seen  measured  by  them. 

4.  Half  a  peck  of  nuts  is  how  many  quarts? 

5.  i  of  a  peck  is  how  many  quarts? 

6.  4  quarts  of  berries  are  what  part  of  a  peck? 

7.  6  quarts  are  what  part  of  a  peck? 

8.  f  of  a  peck  of  oats  are  how  many  quarts? 

9.  John  sowed  |^  of  a  peck  of  blue-grass  seed;  how  many 
quarts  were  left  out  of  a  peck? 

99.  Four  pecks  make  a  bushel. 

1.  ^  a  bushel  of  potatoes  is  how  many  pecks? 

2.  I  of  a  bushel  are  how  many  pecks? 

3.  Half  a  bushel  of  cranberries  is  how  many  quarts? 

4.  Two  bushels  are  how  many  pecks? 

5.  Estimate  the  capacity  of  a  box  or  basket  brought  into 
the  schoolroom. 

6.  IJ  bushels  of  walnuts  are  how  many  pecks? 

7.  Henry  gathered  a  bushel  of  beans  from  his  garden, 
and  sold  half  of  them  for  25  cents  a  peck;  how  much  money 
did  he  receive? 

100.  Grains,  fruits,  vegetables,  and  some  other  things 
that  are  not  liquids,  are  sold  by  these  measures.  They  are 
called  Dry  Measures. 

2  pints  (pt.)  =  1  quart  (qt.)- 
8  quarts  =  1  peck  (pk.). 
4  pecks         =  1  bushel  (bu.). 


MISCELLANEOUS  PROBLEMS.  81 

MISCELLANEOUS  PROBLEMS. 

101.  1.  How  many  feet  are  there  in  a  yard?  How 
many  inches  in  a  yard? 

2.  ^  of  a  yard  is  how  many  inches?     How  many  feet? 

3.  We  have  a  measure  which  holds  just  8  quarts;  what 
is  the  measure  called?  How  many  quarts  are  there  in  a 
peck  of  corn? 

4.  A  party  of  boys  went  nutting  and  gathered  2\  pecks 
of  nuts;  how  many  quarts  did  they  have? 

5.  32  quarts  of  strawberries  are  how  many  gallons? 

6.  At  6  cents  a  yard,  how  many  yards  of  muslin  can  you 
buy  for  72  cents? 

7.  How  many  spools  of  thread  can  I  buy  for  35  cents, 
at  5  cents  a  spool?  How  many  at  4  cents  a  spool,  and  how 
many  cents  remaining? 

8.  ^  of  24  acres  of  land  is  planted  in  sugar-corn,  \  in 
potatoes,  \  in  oats,  and  the  remainder  in  meadow;  how 
many  acres  are  planted  in  meadow? 

9.  A  man  is  rowing  down  the  river  8  miles  an  hour;  at 
that  rate,  how  long  will  he  be  in  going  48  miles? 

10.  At  4  cents  a  pound,  how  many  pounds  of  oatmeal 
can  you  get  for  60  cents? 

11.  12  bushels  are  how  many  pecks? 

12.  How  many  quarts  are  there  in  5  pecks? 

13.  A  boy  earned  $1.65,  and  his  father  gave  him  35  cents; 
he  paid  50  cents  for  a  scrapbook;  how  much  money  had  he 
left? 

14.  Bought  10  yards  of  cloth  at  4  dollars  a  yard,  and  sold 
it  for  $8  less  than  I  gave  for  it;  how  much  did  I  get 
for  it? 


82  MISCELLANEOUS  PROBLEMS. 

15.  A  boy  earned  75  cents  a  day,  and  paid  50  cents  a  day 
for  his  board;  how  much  did  he  save  each  day? 

16.  How  much  did  this  boy  save  in  6  days? 

17.  Max  has  a  quarter  of  a  dollar,  a  dime,  a  5-cent  piece; 
how  much  money  has  he? 

18.  James  has  J  as  much  money  as  Max;  how  nmch  has 
he? 

19.  We  paid  for  a  Christmas  tree,  $2;  for  tapers,  40 
cents;  for  candy,  75  cents;  for  netting  for  candy  bags,  10 
cents;  for  toys,  $1.20;  for  books,  $3.60;  what  did  all  cost? 

20.  How  many  yards  of  fringe  will  be  needed  to  go 
round  a  rug  5  ft.  long  and  3  ft.  wide?     (Make  a  drawing.) 

21.  A  class  of  children  made  69  holly  wreaths  to  trim  a 
schoolroom,  and  used  all  but  10;  how  many  did  they  use? 

22.  If  I  of  a  yard  of  ribbon  costs  2  cents ,  what  is  the  cost 
of  a  yard?    How  many  yards  can  I  buy  for  48  cents? 

23.  A  man  bought  60  boxes  of  peaches,  but  found  {  of 
them  unsound;  how  many  boxes  were  sound? 

24.  Mary's  aunt  gave  her  a  doll  for  which  she  paid  $4; 
for  the  doll's  house  she  bought  a  set  of  chairs  for  which  she 
paid  $1.50,  a  sofa  for  $1,  a  bedstead  for  $1.20,  and  a  little 
bureau  for  90  cents;  what  did  all  cost? 

25.  How  many  feet  must  a  boy  walk  in  going  around 
this  lot? 


51.  ft 


SSft, 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.  83 

ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

103.  2  +  8. 

Make  a  table,  adding  2  to  numbers  ending  in  8.  Add  8 
to  numbers  ending  in  2. 

Make  a  table,  subtracting  2  from  the  results  of  this 
addition.     Subtract  8  from  each  of  these  results. 

Copy  and  add: 

(1)      (2)      (3)      (4)      (5)      (6)      (7)      (8)      (9)    (10) 

91  98  97  89  86  82  89  78  97  95 

17  12  12  28  12  29  18  22  12  12 
22  81  78  82  11  81  72  89  89  79 
68  27  22  29  87  28  29  21  21  21 
22  92  89  91  22  12  91  98  98  80 

18  18  21  18  18  19  18  10  12  28 
72  82  91  82  72  81  82  82  82  92 
24  22  12  26  28  28  26  29  25  16 
88  69  88  95  84  45  87  87  89  86 
78998969889777748488 

Add: 

11.  27,  62,  29,  81,  28,  12,  75,  27,  88,  and  80. 

12.  68,  22,  89,  21,  98,  12,  80,  28,  63,  and  99. 

103.  2  +  9. 

Add: 

2  12  22  32  42  52  62  72  82  92 
9999999999 


84  ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

9    19    29    39    49    59    69    79    89    99 
2222222222 


Make  a  table,  subtracting  9  from  each  of  the  results 
obtained  above.     Subtract  2  from  each. 

Add: 

9,  2,   8,  2,  1,  9,  1,  9,  1,  9,  1,  9,  1,  9,  8,  2. 

6,  6,  9,  1,  9,  1,  9,  1,  6,  2,  2,  6,  1,  1,  7,  2. 

9,  9,  2,  2,  9,  1,  9,  1,  9,  9,  2,  9,  9,  2,  2,  2. 

8,  4,  9,  9,  2,  9,  1,  7,  2,  9,  2,  6,  2,  9,  2,  7. 

Copy  and  add: 

(1)  (2)   (3)   (4)   (5)   (6)  (7)   (8)  (9)  (10) 

89  89  99  89  99  29  89  82  72  89 

22  28  81  29  81  69  92  97  21  20 

98  12  28  92  28  22  99  21  97  99 
92  79  92  99  92  89  19  99  92  92 
29  29  99  29  99  29  92  92  29  29 

99  92  29  92  29  92  28  29  89  92 
92  99  12  91  82  99  92  91  22  91 
29  29  22  22  24  29  19  25  94  24 
54  68  49  98  67  65  65  97  18  97 
97847959897786584857 

Add: 

11.  29,  79,  22,  98,  92,  29,  99,  92,  28,  99,  and  43. 

12.  98,  82,  29,  99,  92,  29,  92,  96,  29,  64,  and  80. 


OUNCES  AND  POUNDS. 


85 


EXERCISE. 

04. 

Find  the  differences: 

1. 

8013- 

-    334=? 

15. 

8054- 

-3505=? 

2. 

7321- 

-  233=? 

16. 

7033- 

-2204=? 

3. 

8122- 

-   124=? 

17. 

7021- 

-3402=? 

4. 

6124- 

-  334=? 

18. 

9041- 

-  405=? 

5. 

9324- 

-  405=? 

19. 

2043- 

-  535=? 

6. 

8432- 

-  445=? 

20. 

7040- 

-  534=? 

7. 

6242- 

-2345  =  ? 

21. 

7031- 

-  435  =  ? 

8. 

6301- 

-3444=? 

22. 

6304- 

-1325  =  ? 

9. 

6413- 

-1434=? 

23. 

5402- 

-3444=? 

10. 

8234- 

-1135=? 

24. 

5204- 

-2245=? 

11. 

8012- 

-  245  =  ? 

25. 

5302- 

-  325=? 

12. 

4210- 

-  245=? 

26. 

9303- 

-5454=? 

13. 

6243- 

-2345=? 

27. 

9000- 

-2001  =  ? 

14. 

8544- 

-2035  =  ? 

28. 

9011- 

-7017  =  ? 

OUNCES  AND  POUNDS. 


105.  1.  If  I  put  the  pound  weight  on  one  side  of  the 
scales,  how  many  ounces  must  I  put  on  the  other  side  to 
balance  it?  A  pound  is  16  ounces. 


86  MISCELLANEOUS  PROBLEMS. 

2.  J  of  a  pound  is  how  many  ounces? 

3.  If  I  wish  to  buy  a  quarter  of  a  pound  of  tea,  how  many 
ounces  must  be  put  upon  the  scales  to  balance  it? 

4.  4  ounces  of  ginger  arc  what  part  of  a  pound? 

5.  At  5  cents  an  ounce,  what  will  i  of  a  pound  of  celery 
seed  cost? 

6.  At  2  ounces  for  5  cents,  how  many  ounces  of  pepper 
can  be  bought  for  20  cents? 

7.  \\  pounds  of  figs  are  how  many  ounces? 

8.  f  of  a  pound  of  maple  sugar  are  how  many  ounces? 

16  ounces  (oz.)=  1  pound  (lb.). 

106.  MISCELLANEOUS   PROBLEMS. 

1.  A  man  paid  $72  for  a  wagon  and  $8  for  repairs,  then 
sold  it  so  as  to  gain  $9;  how  much  did  he  receive  for  it? 

2.  Three  men  bought  a  horse,  the  first  man  paying  $36, 
the  second  man  $15,  and  the  third  man  as  much  as  the  first 
two;  how  much  did  the  horse  cost? 

3.  If  I  buy  11  yards  of  velvet  at  $3  a  yard,  and  sell  it  at 
$4  a  yard,  how  much  shall  I  gain? 

4.  If  a  man  earns  $12  a  week  and  spends  $7,  how  much 
will  he  save  in  6  weeks? 

5.  Willie  gathered  a  bushel  of  chestnuts;  he  gave  his 
brother  10  quarts,  kept  6  quarts,  and  sold  the  remainder; 
how  many  quarts  did  he  sell? 

6.  When  Alfred  reads  8  pages  more  he  will  have  finished 
his  story  book,  which  contains  90  pages;  how  many  pages 
has  he  read? 

7.  A  man  gave  a  watch  and  $10  in  money  for  a  horse 
worth  $75;  what  is  the  value  of  the  watch? 


MISCELLANEOUS  PROBLEMS.  87 

8.  Two  persons  start  from  the  same  point  and  travel  in 
opposite  directions;  one  travels  26  miles  and  the  other  38 
miles;  how  far  apart  are  they? 

9.  A  man  saved  24  dollars  one  month,  half  as  much  the 
next  month,  and  6  dollars  the  third  month;  how  much 
money  had  he  saved  at  the  end  of  the  three  months? 

10.  If  82  feet  of  wire  are  already  used  in  making  a  fence, 
and  9  feet  more  are  needed,  how  much  wire  will  be  used? 

11.  James  shoots  an  arrow  which  does  not  reach  the 
mark  by  9  feet.  If  the  mark  is  51  feet  away,  how  far  is  the 
arrow  from  James?     (Make  a  drawing.) 

12.  Two  persons  start  from  the  same  place  and  travel  in 
the  same  direction;  one  travels  40  miles  an  hour,  and  the 
other  35  miles  an  hour;  how  far  apart  will  they  be  in  1  hour? 
(Show  by  drawing  )     How  far  in  6  hours? 

13.  Charles  gets  $6  a  month  for  selling  a  daily  paper; 
Henry  gets  \  as  much  for  selling  a  weekly  paper;  how  much 
will  both  have  earned  in  5  months? 

14.  From  a  chest  of  tea  containing  60  pounds,  9  pounds 
v/ere  sold  at  $1  a  pound;  what  was  the  value  of  the  re- 
mainder, at  the  same  rate? 

15.  I  bought  a  bushel  of  tomatoes  for  70  cents,  a  half- 
bushel  of  turnips  for  20  cents,  and  a  peck  of  beans  for  10 
cents;  what  I  paid  for  all  was  half  the  cost  of  a  barrel  of 
potatoes.     What  did  the  potatoes  cost? 

16.  A  box  contains  134  oranges,  and  a  barrel  contains 
64  more  than  the  box;  how  many  oranges  does  the  barrel 
contain? 

17.  I  bought  a  horse  and  sleigh  for  $150;  the  sleigh  cost 
$45;  what  did  the  horse  cost? 

18.  After  spending  $80  for  a  pony,  George  found  that  he 


88  ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

had  $65  left  in  his  savings  bank;  how  much  money  had  he 
at  first? 

19.  In  an  orchard  there  are  150  apple  trees;  this  is  50 
more  than  the  number  of  peach  trees;  how  many  peach 
trees  are  there? 

20.  A  man  having  190  young  orange  trees,  bought  89 
more,  and  then  sold  50;  how  many  had  he  left? 

21.  Add  three  hundred  nine  to  seven  hundred  eleven, 
and  subtract  twenty-nine  from  the  sum. 

22.  A  farmer  bought  40  sheep  for  144  dollars  at  one  time, 
and  50  sheep  for  155  dollars  at  another  time;  how  much  did 
the  sheep  cost  him? 

23.  A  boy  shot  an  arrow  145  feet  up  the  road,  and  another 
149  feet  down  the  road;  how  far  were  the  arrows  apart? 
(Make  a  drawing.) 

24.  What  will  150  tons  of  coal  cost,  at  $6  a  ton? 

ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

107.  Make  a  table,  adding  3  to  numbers  ending  in  3. 
What  is  the  ending  figure  of  each  sum? 

Add  3  to  numbers  ending  in  4. 

Add  3  to  numbers  ending  in  5.  What  is  the  ending  figure? 
Make  subtraction  tables,  taking  3  from  the  results  ob- 
tained in  each  of  the  three  addition  tables  above. 

108.  3  +  6. 

Add,  beginning  at  the  left: 

O,     o,     ^,     O,     o,     iU,     O,     o,     ^,     o,     O,     ^,     O,     o,     ^. 

9,   6,   3,   2,    3,   5,    1,   2,   2,   5,   2,   5,    3,    2,   5. 
8,   7,   3,   2,   5,   3,   1,   2,   4,   3,   2,   3,   5,   1,   2. 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.  89 

Add,  beginning  at  the  bottom  of  the  column : 

(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

95  39  53  23  85  99  29  82  55  59 

23  92  39  19  23  92  89  95  22  39 

59  15  99  51  99  29  22  23  92  92 

31  23  92  32  91  91  12  29  92  92 

92  52  29  95  22  12  55  59  23  25 

95  35  91  13  95  25  33  32  94  23 
23  93  12  21  13  53  12  92  10  59 
22  24  25  32  24  38  23  24  24  39 
59  68  57  48  58  64  57  56  57  54 
99988679989878987998 

109.  3  +  6. 

Add: 

(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

66  36  89  38  52  99  26  69  29  96 
33  83  22  99  31  21  63  92  62  29 

91  29  66  92  16  66  39  26  36  62 
26  92  33  26  63  33  92  63  93  36 
63  26  99  13  31  99  23  39  29  93 
39  63  29  69  96  22  36  92  32  29 

92  32  62  32  23  67  56  99  68  69 
26  93  36  96  32  36  27  23  27  36 

67  97  55  95  59  67  67  68  67  58 

96  88  99  78  79  99  90  89  67  98 


110.  3  +  7. 

Make  a  table,  adding  7  to  numbers  ending  in  3  and  3  to 
numbers  ending  in  7. 


90  ADDITION  AND  SUBTRA CTION  BY  ENDINGS. 

Make  a  table,  subtracting  7  from  the  results  of  the  ad- 
dition tables.  Subtract  3  from  the  same  numbers. 
Add: 

9,   9,   2,   3,  7,   2,   9,   9,   3,    7,    3,   6,  2,   9,   3,    7. 

6,   6,    7,   2,  9,    3,    7,    2,   9,   9,    3,    7,  2,   9,   9,   5. 

9,    7,   4,    3,  7,    2,   9,   9,    3,    6,    2,   9,  3,    7,   2,   9. 

8,    7,   5,   2,  9,   9,    3,    7,   3,   6,   2,   9,  3,   5,   2,   3. 

Add: 

(1)      (2)  (3)      (4)      (5)      (6)      (7)      (8)  (9)     (10) 

69  99  99  92  99  62  29  96  73  78 

32  79  22  26  99  36  90  73  37  32 

76  32  56  73  29  73  22  39  93  97 

33  96  33  39  82  30  68  19  99  93 

77  24  99  99  27  99  32  92  20  29 
33  97  29  22  73  9  77  97  9  72 
99  73  62  63  30  92  33  23  72  36 

9  32  37  38  65  23  92  57  38  95 

96  89  74  79  6  98  99  7  65  98 
66697980996979969770 

REVIEW. 

111.  Add: 

(1)  (2)  (3)  r4)   (5)   (6)   (7)   (8)  (9)  (10) 

57  17  28  28  97  16  52  55  86  58 

73  42  42  53  32  51  37  42  73  22 

32  53  33  36  52  32  31  28  39  29 

26  37  35  81  26  97  59  52  11  61 

62  51  33  22  92  11  21  31  78  23 

23  23  43  35  17  29  27  35  22  37 

89  89  98  57  98  76  55  68  21  42 

88  97  86  96  85  85  98  86  24  35 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.        91 


EXERCISE. 


113.  Subtract: 

(1) 

(2)       (3) 

(4) 

(5) 

(6) 

5514 

5065   7617 

708 

8119 

8004 

1445 

5050   3455 

3055 

5505 

4345 

7. 

8301-2034 

13. 

7322- 

-6543 

8. 

9312-3543 

14. 

6411- 

-5524 

9. 

6431-2332 

15. 

3501- 

-3032 

10. 

8433-3544 

16. 

8032- 

-6503 

11. 

9441-5034 

17. 

9020- 

-5003 

12. 

9400—3623 

18. 

8042- 

-5604 

Find  the  differences : 

19. 

9000-1445 

28. 

8122- 

-4435 

20. 

8000-4405 

29. 

5333- 

-1045 

21. 

3111-2445 

30. 

7303- 

-4045 

22. 

5111-2405 

31. 

4313- 

-4144 

2-3. 

7011-4435 

32. 

5113- 

-4245 

24. 

9112-4345 

33. 

9313- 

-4344 

25. 

7414-4425 

34. 

8041- 

-1445 

26. 

4444-3345 

35. 

5414- 

-1415 

27. 

9041-4445 

36. 

8434- 

-1435 

CLASS    EXERCISE. 
113.  Note. — Each  pupil  should  subtract  one  number. 

9602410131120561  17954362801756 

5254443513453545  7932425360939 


92  MISCELLANEOUS  PROBLEMS. 

MISCELLANEOUS   PROBLEMS. 

114.  1.  James  has  9  cents,  and  John  has  three  times 
as  many  less  6;  how  many  has  John? 

2.  One  day  a  man  traveled  25  miles  by  railroad,  34  miles 
by  steamboat,  and  returned  10  miles;  how  far  was  he  then 
from  his  starting  place? 

3.  I  bought  4  yards  of  silk  at  $2  a  yard,  and  2  shawls  at 
$10  each;  how  much  change  ought  I  to  receive  from  2 
twenty-dollar  bills? 

4.  A  grocer  paid  $165  for  30  barrels  of  flour,  and  $50  for 
20  barrels  of  potatoes;  how  much  did  he  pay  for  both? 

5.  A  boy  who  had  53  marbles  loaned  20,  and  afterwards 
borrowed  9  more;  how  many  marbles  had  he  then? 

6.  A  boy  paid  $20  for  a  team  of  goats,  $8  for  his  carriage, 
and  $4  for  harness;  he  sold  them  so  as  to  lose  $4;  for  how 
much  did  he  sell  them? 

7.  I  bought  3  yards  of  cloth  at  $7  a  yard,  for  a  coat;  the 
buttons  and  cord  cost  $2,  and  the  making  of  it  $10;  what 
was  the  cost  of  the  coat? 

8.  A  pole  is  40  feet  long.  If  J  of  it  is  in  the  ground,  and 
the  rest  in  the  air,  how  many  feet  are  in  the  air? 

9.  A  man  gave  a  carriage  and  $110  in  money  for  a  lot 
worth  $400;  what  was  the  value  of  the  carriage? 

10.  Some  children  returned  from  the  lake  with  a  basket 
of  shells;  after  giving  half  of  them  away,  they  had  95  left. 
How  many  had  they  at  first? 

11.  A  party  of  school  children  went  to  Fairview  Park. 
$1.75  is  50  cents  less  than  they  paid  for  carfare;  how  much 
did  they  pay? 

12.  John  bought  a  pack  of  shingles,  and  used  175  in 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.        93 

mending  the  roof.     He  had  75  left;  how  many  did  the  pack 
contain  at  first? 

13.  A  farmer  having  $156  paid  one-half  of  his  money 
for  a  horse,  and  one-half  of  the  remainder  for  a  cow;  how 
much  did  each  cost? 

14.  How  much  money  has  the  farmer  left  after  paying 
for  both  horse  and  cow? 

115.  3  +  8. 

Make  a  table,  adding  8  to  numbers  ending  in  3,  and  3  to 
numbers  ending  in  8. 

Write  the  results  of  the  addition  above  and  subtract  8 
from  each.     Subtract  3  from  each  number. 

Add: 

6,  7,   8,   2,   8,   9,   3,   8,   9,   3,   8,   9,   3,   8,   9. 
9,   9,    3,   9,    3,   8,   9,    2,   9,   9,    3,    S,   9,   0,   9. 

7,  4,   9,    3,    8,   9,    3,    8,   9,    2,   9,   9,    0,    3,    7. 
9,   8,    3,    3,    7,    3,    8,   9,    2,    9,   9,    3,    7,    3,   8. 

Add: 

(1)      (2)      (3)       (4)      (5)      (6)      (7)      (8)      (9)     (10) 

82  30  93  89  88  59  93  7  89  90 

39  99  99  32  33  32  99  87  32  23 

93  8  89  76  97  99  29  33  9  69 

87  83  32  33  83  98  72  79  78  8 

39  37  99  7  39  23  37  28  33  33 

72  93  98  93  78  97  93  82  97  79 

29  99  23  89  33  83  89  32  83  33 

8  23  94  38  99  36  38  93  33  99 

86  59  89  65  94  57  56  8S  58  89 

77  99  77  88  67  97  97  88  99  80 


94        ADDITION  AND  SUBTRACTION    BY  ENDINGS. 

Add: 

11.  99,  78,  33,  97,  93,  29,  98,  83,  38,  44,  and  98. 

12.  88,  33,  99,  89,  32,  99,  92,  28,  98,  84,  and  69. 

13.  Find  the  sum  of:  93,  35,  33,  53,  94,  39,  43,  43,  77, 
and  98. 

14.  62  +  39  +  89  +  23  +  93  +  35  +  43  +  43  +  87  +  77=? 

116.  3  +  9. 

Add: 

3     13    23    33    43    53    63    73    83    93 


9 

9 

9 

9 

9      9      9 

9      9 

9 

9 
3 

19 
3 

29 
3 

39 
3 

49    59    69 
3      3      3 

79    89 
3      3 

99 
3 

Make  a  subtraction  table,  taking  9  from  each  of  the 
results  of  addition  above.     Subtract  3  from  each  number. 

Add;  beginning  at  the  left: 

9,  4,  9,  8,  2,  9,  9,  3,  9,  8,  3,  8,  9,  9,  1. 

y,  y,  o,  y,  o,  y,  y,  y,  o,  y,  o,  o,  y,  y,  y. 

8,  5,  9,  9,  9,  3,  7,  3,  8,  9,  3,  9,  8,  0,  9. 

8,  9,  3,  3,  7,  3,  8,  9,  3,  9,  7,  2,  9,  9,  2. 

51+9=?  62  +  7=?  72-3  =  ?  70-2  =  ? 

72  +  6=?  73  +  7  =  ?  91-2=?  90-1  =  ? 

81  +  8=?  92  +  8=?  81-3=?  80-3=? 

83  +  9=?  93  +  5=?  32-3=?  91-3=? 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.  95 

Add: 

(1)      (2)       (3)      (4)      (5)       (6)      (7)      (8)      (9)    (10) 

99  99  89  99  89  99  90  8  88  97 

93  38  39  39  93  99  39  39  93  99 

30  93  93  79  39  39  99  83  99  33 

78  77  99  33  98  93  93  99  39  99 

99  30  98  99  93  89  29  39  99  89 

33  89  33  98  97  38  99  92  83  32 

9  93  9  93  33  93  82  89  37  86 

99  8  83  37  93  24  37  35  6  90 

96  33  99  54  98  67  55  86  57  6 

6659  69  89696998609078 

Add: 

11.  98,  89,  33,  79,  39,  80,  9,  92,  38,  98,  and  54. 

12.  99,  20,  83,  97,  33,  99,  8,  83,  34,  78,  and  78. 

13.  Find  the  sum  of:  3,  35,  39,  53,  94,  34,  49,  43,  89, 
and  79. 

14.  95  +  39  +  33  +  45  +  83  +  39  +  63  +  34  +  97  +  67  =  ? 


EXERCISE. 

117.  Find  the  differences  • 

1.  9453-   545=?  8.  3323-2554=? 

2.  8453-   544=?  9.  9203-3405=? 

3.  9341—5445  =  ?  10.  8801-   134=? 

4.  8341-5345  =  ?  11.  7640-2534=? 

5.  9623-3545=?  12.  3141-2445=? 

6.  7344-3545=?  13.  3001-2154=? 

7.  6412-4534=?  14.  6011-5403=? 


96    COMPARISON  OF  HALVES,  FOURTHS  AND  EIGHTHS. 


15. 

3043-1415=? 

23. 

7004- 

-1345  =  ? 

16. 

8001—5045=? 

24 

9043- 

-1534=? 

17. 

7002—5435  =  ? 

25 

3842- 

-1435=? 

18. 

4003-3004  =  ? 

26. 

5101- 

-4434=? 

19. 

6301-4345=? 

27. 

8600- 

-5534=? 

20. 

7304-3025=? 

28. 

8122- 

-6035  =  ? 

21. 

9801-  534=? 

29. 

5043- 

-1415=? 

22. 

8074-2135=? 

30. 

4312- 

-  243  =  ? 

118. 

Find  the  differences: 

1. 

26345-2556=? 

10. 

59203- 

-2505  =  ? 

2. 

15043-1546=? 

11. 

68304- 

-1056=? 

3. 

19411-1506  =  ? 

12. 

70005- 

-6056=? 

4. 

27522-3615=? 

13. 

20003- 

-2455=? 

5. 

35432-4546=? 

14. 

49503- 

-4546=? 

6. 

43543-1456  =  ? 

15. 

30533- 

-     36=? 

7. 

23543-1554=? 

16. 

30334- 

-3455=? 

8. 

50354-5646  =  ? 

17. 

23451- 

-     56=? 

9. 

47352-4353  =  ? 

18. 

10052- 

-1554  =  ? 

COMPARISON  OF  HALVES,  FOURTHS,  AND  EIGHTHS. 


x^ 

~%\ 

\"s\ 

/%\ 

V's/ 

\'/s) 

\\ 

jy 

119.  1.  A  whole  melon  can  be  divided  into  how  many- 
halves?    How  many  fourths? 


COMPARISON  OF  HALVES,  FOURTHS,  AND  EIGHTHS.    97 

2.  Fold  a  paper  square  into  two  equal 
triangles.  One  of  the  triangles  is  what  part 
of  the  whole  square? 

3.  Fold  the  same  square  so  as  to  make 
four  equal  triangles.  What  part  of  the 
whole  square  is  one  of  the  small  triangles? 

4.  i  is  equal  to  how  many  fourths? 

5.  i  and  {  make  how  any  fourths? 

6.  i  and  f  equal  how  many  fourths? 

7.  Fold  your  square  so  as  to  make  eight  equal  triangles. 
One  of  the  triangles  is  what  part  of  the  whole  square?  Two 
of  the  triangles  are  what  part  of  the  whole? 

8.  If  three  of  the  triangles  were  cut  out  of  the  square, 
what  part  of  the  whole  would  be  left? 

9.  i  of  the  square  is  equal  to  how  many  eighths?  ^  is 
equal  to  how  many?    |  are  equal  to  how  many  eighths? 

10.  I  of  a  whole  cheese  are  equal  to  how  many  eighths  of 
the  cheese? 

11.  I  +  I  are  how  many  eighths?     4  +  1  =  ? 

12.  l^  +  f  are  how  many  eighths? 

Note. — Use  objects  freely  in  the  work  with  fractions. 

130.  1.  From  your  folded  squares  find  the  answers  to 
the  following  questions : 

Kf=?  l-i=?  i-i=?  i-i=? 
l+i=?  |-|=?  *-i=?  i-f=? 
i+t=?       l-i=?       i-f=?       i-t=? 

2.  Draw  a  square  and  divide  it  into  eight  equal  oblongs; 
find  from  the  drawing  the  answers  to  the  following  ques- 
tions : 


98    COMPARISON  OF  HALVES,  FOURTHS,  AND  EIGHTHS. 

2  times  i  =  ?  |X3=?  iX4  =  ? 

|X5  =  how  many  wholes? 

-     2  times  f  =  ?  tX2  =  ?  iX3=? 

|X3  =  how  many  wholes? 

2  times  t=?  |X2  =  ?  fX2  =  ? 

1X2  =  how  many  wholes? 

4X4=?  iX3=?  iofi  =  ? 

|X4=?  iofi  =  ?  fX2=? 

iX2  =  ?  iofi  =  ?  iX4=? 

3.  Mary  made  a  cake  for  tea;  half  of  it  was  eaten,  and 
the  remainder  was  divided  equally  among  four  visitors. 
What  part  of  the  whole  cake  did  each  visitor  receive? 

4.  George  had  a  ball  of  twine  for  his  kite ;  he  used  half  of 
it,  and  divided  the  remainder  equally  between  two  other 
boys.  What  part  of  the  whole  ball  of  twine  did  each  boy 
get? 

131.  Take  two  equal  squares  of  paper.  Fold  each  into 
four  equal  smaller  squares;  call  them  square  crackers,  and 
give  them  to  four  children,  so  that  they  shall  have  equal 
shares. 

Note. — Distribute  all  the  parts  of  one  square  first. 

1.  What  part  of  the  two  large  squares  does  each  child  re- 
ceive? 

2.  What  part  of  one  square? 

3.  To  how  many  children  did  you  give  the  two  squares? 

4.  One  of  the  four  equal  parts  of  anything  is  called  what? 
Place  the  small  squares  together  again  so  as  to  form  the 

two  large  squares. 


COMPARISON  OF  HALVES,  FOURTHS,  AND  EIGHTHS.    99 

5.  J  of  2  squares  is  what  part  of  one  of  the  squares? 

6.  i  of  2  pies=  ?     i  of  2  apples-  ?     i  of  2  melons  =  ? 

7.  Divide  two  sticks  of  candy  equally  among  four  boys. 
What  part  of  the  whole  will  each  boy  receive?  What  part 
of  one  stick  is  that? 

133.  Take  three  equal  squares  of  paper.  Divide  these 
equally  among  four  children.  (Fold  each  into  four  smaller 
squares.) 

1.  What  part  of  the  three  large  squares  does  each  child 
receive? 

2.  What  part  of  one  square? 

3.  Into  how  many  equal  parts  did  you  divide  the  three 
squares? 

4.  One  of  these  equal  parts  is  called  what? 

Place  the  small  squares  together  again  so  as  to  form  the 
three  large  squares  you  had  at  first. 

5.  I  of  3  squares  is  what  part  of  one  square? 

6.  What  part  of  one  whole  toothpick  is  ^  of  3  tooth- 
picks? 

7.  Divide  3  oranges  equally  among  4  boys.  What  part 
of  the  3  will  each  receive?     |  of  3  is  what  part  of  1? 

8.  Suppose  you  plant  3  potatoes  in  4  hills.  If  you  divide 
them  equally,  what  part  of  1  potato  will  be  in  each  hill? 
(Make  a  picture  to  show  this.) 

9.  Give  3  bananas  to  4  girls,  dividing  them  equally;  what 
will  each  girl  receive? 

10.  If  you  divide  23  melons  equally  among  4  boys,  what 
is  each  boy's  share?     (Picture.) 

11.  I  wish  to  put  27  quarts  of  blackberries  into  4  jars, 
putting  the  same  number  of  quarts  into  each;  how  many 
quarts  will  each  jar  contain? 


100  MULTIPLICATION  AND  DIVISION. 

MULTIPLICATION  AND  DIVISION. 

133.  Copy  and  learn: 

7X7  =  49  lOX  7  =  70  8X  8  =  64  llx  8  =  88 

8X7  =  56  llx  7  =  77  9X  8  =  72  12x  8  =  96 

9X7  =  63  12X  7  =  84  lOX  8  =  80  8X11  =  88 

7X8  =  56  7X10  =  70  8X  9  =  72  7X12  =  84 

7X9  =  63  7X11  =  77  8X10  =  80  8X12  =  96 

Recite  the  division  table  from  the  multiplication  table. 

MENTAL    EXERCISE. 

134.  1.  How  many  desks  are  there  in  a  schoolroom 
which  has  7  rows  of  desks,  and  7  desks  in  each  row? 

2.  If  a  pair  of  curtains  cost  7  dollars,  what  will  9  pairs 
cost? 

3.  Eight  boys  are  building  a  snow  fort;  if  each  makes 
7  balls  of  snow,  how  many  balls  will  they  have  in  all? 

4.  What  is  the  cost  of  8  yards  of  muslin  at  8  cents  a  yard? 

5.  One  peck  is  how  many  quarts?  John  gathered  9 
pecks  of  chestnuts;  how  many  quarts  had  he? 

6.  If  8  loaves  of  bread  are  used  in  one  week,  how  long 
will  96  loaves  last? 

7.  If  melons  are  selling  at  8  cents  each,  what  will  9  cost? 

8.  May  had  75  cents  to  spend  for  lace  at  8  cents  a  yard; 
how  many  yards  did  she  buy?  How  many  cents  had  she 
left? 

9.  At  8  dollars  a  ton,  how  many  tons  of  coal  can  be 
bought  for  96  dollars? 


FINDING  ONE  OF  THE  EQUAL  PARTi^jQJ^\XWM¥^^^i^rX^l' 

10.  At  7  cents  a  roll,  how  many  rolls  of  wall  paper  can 
be  bought  for  56  cents? 

11.  Make  problems  for: 


10X8  =  80 

12X7  =  84 

88-^8  =  ll 

56^7  =  8 

11X7  =  77 

12X8  =  96 

70-^7  =  10 

63-^-7=9 

Note. — Do  this  in  class. 

Finding  One  of  the  Equal  Parts  of  a  Number. 

EXERCISE. 

135.  1.  If  9  melons  cost  72  cents,  what  is  the  cost  of 
one  ? 

2.  One  man  working  alone  can  do  a  piece  of  work  in  56 
hours;  in  how  many  hours  can  7  men  do  the  work? 

3.  If  8  tons  of  coal  cost  72  dollars,  what  is  the  cost  of  a 
ton? 

4.  I  paid  96  cents  for  8  dozen  eggs;  how  much  were  they 
a  dozen? 

5.  If  one  man  works  alone,  it  will  take  63  hours  to  dec- 
orate a  hall;  if  9  men  work  together,  in  how  many  hours 
can  the  work  be  done? 

6.  A  merchant  paid  84  dollars  for  12  rugs;  at  that  rate, 
what  was  paid  for  one  rug? 

7.  Mary  paid  96  cents  for  12  dozen  buttons;  how  much 
were  they  a  dozen? 

8.  64  trees  were  planted  in  8  equal  rows ;  how  many  were 
planted  in  one  row? 

9.  How  many  pecks  are  there  in  72  quarts? 

10.  A  man  earned  84  dollars  in  7  weeks;  at  that  rate, 
how  many  dollars  did  he  earn  in  one  week? 


«>©• 
"S', 


J  IX^Z  m^'Bim  (iNp,  QF  THE  EQUAL  PARTS  OF  A  NUMBER. 

11.  How  many  cents  are  there  in  half  a  dollar?     In  J  of 
a  dollar?    In  i^j^?    J? 

12.  25  cents  is  what  part  of  $1?    20  cents  is  what  part 
of  $1? 

13.  f  of  $1  are  how  many  cents?     |  of  $1?     f  of  $1?     |? 

14.  Frank  spent  tV  of  a  dollar  for  pencils  and  J  of  a  dollar 
for  drawing  paper;  how  much  money  did  he  spend? 

15.  Helen  spent  f  of   $1    for   muslin,  and  i  of  $1  for 
thread;  how  many  cents  did  she  spend? 

16.  Make  problems  for: 

^  of  49  =  7        i  of  96  =  12    8)64  bushels  12)96  dollars 

8  bushels  8  dollars 

Jof72  =  9        +of  70=10    7)56  cents  10)80  nails 

8  cents  8  nails 

Note. — Do  this  in  class. 

17.  Begin  with  49  and  find  one-seventh  of  all  numbers 
to  63. 

Thus:  i  of  49  =  7.    |  of  50  =  7  and  1  remaining.     ^  of  51  =  7 
and  2  remaining,  etc. 

18.  Find  one-eighth  of  all  numbers  from  64  to  88. 

126.  TABLES    FOR    REVIEW. 

1X6=  6  1X7=  7  1X8=  8 

2X6  =  12  2X7  =  14  2X8=16 

3X6  =  18  3X7  =  21  3X8  =  24 

4X6  =  24  4X7  =  28  4x8  =  32 

5X6  =  30  5X7  =  35  5x8  =  40 

6X6  =  36  6X7  =  42  6X8  =  48 


MULTIPLYING  AND  DIVIDING  BY  7  AND  8.       108 


7X6=42 

7X7  =  49 

7X8  =  56 

8X6  =  48 

8X7=56 

8X8  =  64 

9X6  =  54 

9X7  =  63 

9X8=72 

10X6  =  60 

10X7=70 

10X8=80 

11X6=66 

11X7  =  77 

11X8  =  88 

12X6  =  72 

12X7  =  84 

12X8  =  96 

Without  rewriting,  read  these  with  6,  7,  and  8  first. 


MULTIPLYING  AND  DIVIDING  BY  7  AND  8. 


127.  Multiply  by  7: 


1.  6948             3.  9485 

5. 

6098 

7.  10769 

2.  5769             4.  7906 

6. 

6937 

8.  11894 

Divide  by  7: 

9.  19539           12.  39648 

15. 

54957 

18.  17799 

10.  18049           13.  18563 

16. 

13607 

19.  68009 

11.  17825           14.  28359 

17. 

27620 

20.  67265 

128.  Multiply  by  8: 

1.  3849         3.  6957         5. 

6384 

7.  6094 

9.  8649 

2.  8539         4.  9384         6. 

3947 

8.  7483 

10.  5973 

Divide  by  8: 

11.  41443    13.  56457     15. 

21391 

17.  29019 

19.  62808 

12.  51652     14.  58259     16. 

39036 

18.  78863 

20.  39013 

104  MISCELLANEOUS  PROBLEMS. 


CLASS    EXERCISE. 

139.  Note. — Let  each  pupil  multiply  one  number  by  7  and 
add  the  number  carried  over. 

1.  42952091897634017926 

7 

2.  53104293697012369876 


3.  7)19539021650103121798 

4.  8)51652019098723651904 

MISCELLANEOUS  PROBLEMS. 

1 30.  1.  If  in  half  a  day  a  man  picks  4  bushels  of  apples, 
and  a  boy  2  bushels,  how  many  bushels  will  both  pick  in 
a  day?     In  5  days? 

2.  A  newsboy  having  42  papers,  sold  all  but  i  of  them; 
how  many  did  he  sell?     How  many  had  he  left? 

3.  Henry's  age,  which  is  7  years,  is  1  seventh  of  his 
father's  age;  how  old  is  his  father? 

4.  What  measure  holds  4  pecks?  48  pecks  of  cran- 
berries are  how  many  bushels? 

5.  A  boy  having  45  cents  spent  i  of  his  money  for 
drawing  paper  and  -5^  for  pencils;  how  many  cents  did  he 
spend? 

6.  How  many  wheels  have  six  freight  cars,  if  each  car 
has  8  wheels? 

7.  A  farmer's  boy  fed  to  his  colt  ^  a  peck  of  oats  each  day 
for  eight  days;  how  many  bushels  is  that? 


MISCELLANEOUS  PROBLEMS.  105 

8.  John  had  5  dimes;  he  spent  15  cents  for  stamps,  and 
with  the  remainder  took  7  car  rides;  what  was  each 
fare? 

9.  I  bought  a  steak  weighing  a  pound  and  a  half;  how 
many  ounces  did  it  w^eigh? 

10.  3  pounds  of  coffee  make  how  many  ounces? 

11.  A  bushel  of  wheat  weighs  60  pounds;  how  many 
pounds  does  a  peck  weigh? 

12.  Wheat  bran  weighs  20  pounds  to  the  bushel;  what 
is  the  weight  of  a  peck? 

13.  Does  a  pound  of  wheat  weigh  more  than  a  pound 
of  bran?  Which  is  the  larger  bulk?  (See  problems  11 
and  12.) 

14.  At  6  cents  a  pound,  how  many  pounds  of  rice  can  you 
buy  for  50  cents? 

15.  If  John  gives  3  pecks  of  corn  to  twelve  horses  divid- 
ing it  equally,  how  much  corn  does  each  horse  receive? 

16.  How  many  hours  are  there  in  2^  days? 

17.  If  a  boy  is  3  minutes  late  at  school,  how  many  seconds 
has  he  lost? 

18.  For  our  school  gardens  we  spent  $1.50  for  foliage 
plants,  $2.10  for  geraniums,  $1  for  tulip  bulbs,  and  $2  for 
roses  and  pansies.  How  much  money  had  we  left  out  of 
$10,  after  paying  for  all? 

19.  A  farmer  raises  850  bu.  of  corn,  920  bu.  of  oats,  560 
bu.  of  wheat,  390  bu.  of  barley,  78  bu.  of  buckwheat;  how 
much  grain  has  he  in  all? 

20.  I  had  in  bank  $1125,  and  drew  out  $415;  how  much 
have  I  left  in  bank? 

21.  Johnson  &  Co.,  after  selling  2000  cans  of  sugar  corn, 
had  1500  cans  left;  how  many  cans  were  on  sale  at  first? 


106  REVIEW  OF  ADDITION. 

22.  If  I  have  $230,  how  much  must  I  add  to  it  to  be  able 
to  buy  a  horse  and  buggy  worth  $550? 

23.  A  man  receives  $700  for  his  fruit  crop  this  year, 
which  is  $150  more  than  he  received  last  year;  how  much 
did  he  receive  last  year? 

24.  Add  300  to  500,  and  from  this  sum  subtract  the 
difference  of  the  numbers. 

25.  If  I  borrow  at  one  time  $327,  and  at  another  time 
$783,  how  much  do  I  owe  aft^r  paying  $221? 

26.  The  greater  of  two  numbers  is  419,  and  the  less  244; 
what  is  their  difference? 

27.  Henry's  father  was  born  in  1859;  how  old  is  he 
now? 

28.  The  sum  of  two  numbers  is  650;  one  of  the  numbers 
is  200;  what  is  the  other? 


131.  REVIEW    OF    ADDITION. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

93 

62 

22 

99 

96 

69 

93 

33 

35 

39 

49 

29 

33 

29 

33 

33 

33 

89 

39 

63 

39 

32 

34 

45 

53 

23 

28 

35 

52 

56 

53 

99 

94 

93 

33 

93 

96 

93 

92 

23 

39 

35 

39 

39 

33 

39 

35 

64 

43 

43 

32 

42 

49 

43 

49 

34 

43 

43 

93 

43 

43 

43 

43 

93 

77 

87 

87 

88 

89 

87 

99 

98 

98 

77 

79 

78 

79 

78 

69 

79 

REVIEW  OF  ADDITION.  107 

(9)  (10)         (11)         (12)         (13)         (14)         (15)         (16) 


89 

29 

93 

26 

97 

32 

23 

23 

79 

63 

94 

33 

29 

96 

64 

56 

38 

34 

34 

68 

63 

23 

94 

39 

93 

84 

68 

89 

35 

39 

29 

23 

37 

28 

22 

21 

93 

63 

63 

65 

43 

92 

99 

99 

29 

25 

35 

23 

43 

89 

83 

83 

62 

43 

93 

83 

93 

33 

33 

33 

33 

43 

38 

23 

98 

79 

87 

89 

88 

99 

76 

87 

76 

79 

78 

76 

78 

68 

66 

87 

(17) 

(18) 

(19) 

(20) 

(21) 

(22) 

1   (23) 

(24) 

73 

62 

36 

98 

29 

82 

98 

96 

26 

26 

68 

32 

39 

99 

99 

99 

29 

53 

92 

39 

62 

39 

39 

33 

63 

37 

39 

58 

72 

42 

42 

65 

95 

93 

43 

93 

34 

49 

49 

23 

23 

39 

45 

39 

94 

99 

78 

89 

62 

42 

83 

42 

89 

83 

33 

22 

34 

41 

28 

43 

33 

33 

93 

93 

95 

89 

98 

77 

97 

79 

88 

97 

79 

79 

64 

79 

79 

76 

79 

79 

;25)  (: 

26) 

(27) 

(28) 

(29) 

(30) 

(31) 

(32)   (33) 

(34) 

29 

99 

95 

72 

93 

39 

98 

78   65 

99 

69 

12 

29 

36 

28 

63 

93 

29   99 

39 

22 

37 

29 

72 

53 

34 

33 

79   98 

83 

99 

52 

52 

29 

45 

85 

25 

92   33 

85 

21 

22 

33 

52 

33 

39 

43 

38   72 

34 

33 

93 

42 

46 

66 

29 

32 

49   23 

35 

79 

99 

97 

97 

86 

98 

89 

99   97 

99 

108  MISCELLANEOUS  PROBLEMS. 

(35)  (36)  (37)  (38)  (39)  (40)  (41) 


87 

83 

9 

936 

924 

989 

484 

938 

983 

692 

983 

756 

933 

724 

383 

315 

593 

979 

364 

346 

496 

517 

399 

836 

399 

725 

953 

442 

993 

622 

363 

633 

492 

342 

273 

332  934  743  494  434  373  944 
999  789  998  699  997  798  799 
658    66   878   877   278    367   936 

M'SCELLANEOUS  PROBLEMS. 

132.  1.  I  bought  for  Christmas  presents  a  calendar, 
for  which  I  paid  $1,  a  bronze  inkstand  for  $1.50,  a  paper 
weight  for  90  cents,  and  an  album  for  $2.50;  w^hat  did  I 
pay  for  all? 

2.  I  received  $148  for  fruit  trees,  and  $260  for  shade 
trees;  the  expense  of  raising  the  fruit  trees  was  $40,  and 
the  shade  trees  $50;  what  were  the  profits  on  each? 

3.  Bought  a  house,  lot,  horse,  and  buggy  for  $1400.  If 
I  paid  $600  for  the  lot,  and  $200  for  the  horse  and  buggy, 
how  much  was  paid  for  the  house? 

4.  An  agent  during  the  year  traveled  921  miles  by  rail- 
road and  234  miles  by  boat ;  how  much  farther  did  he  travel 
by  railroad  than  by  boat? 

5.  A  man  had  $5424.  To  his  son  he  gave  $965,  and  the 
remainder  to  his  wife;  what  was  his  wife's  share? 

6.  A  father  and  his  two  sons  earned  $1843  in  a  year, 
the  elder  son  earning  $628,  and  the  younger  $456;  how 
much  did  the  father  earn? 

7.  What  year  will  it  be,  in  10  years  from  this  time?  In 
20  years?    In  150  years? 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.       109 

8.  A  merchant  drew  out  of  bank  $650  one  day,  $327  the 
second,  $474  the  third,  and  then  had  $564  in  bank;  how 
much  money  had  he  in  bank  at  first? 

9.  A  man  bought  23  barrels  of  flour  for  $138,  27  barrels 
for  $135,  and  36  barrels  for  $144;  how  many  barrels  did 
he  buy,  and  how  many  dollars  did  he  pay? 

10.  A  merchant  living  18  miles  out  of  Chicago,  goes  to 
the  city  every  morning  and  returns  in  the  evening;  how 
many  miles  does  he  travel  in  6  days? 

11.  A  shoe  merchant  sold  four  dozen  pairs  of  shoes  for 
$192;  this  is  $24  more  than  they  cost  him;  what  did  they 
cost? 

12.  Holt  &  Co.  sold  620  pairs  of  gloves  this  month,  which 
is  20  pairs  less  than  they  sold  last  month,  how  many  pairs 
were  sold  last  month? 

13.  A  real  estate  agent  sold  6  lots  of  land  for  $9,600; 
if  the  lots  were  of  equal  value,  how  much  did  he  receive 
for  each  ? 


ADDITION   AND    SUBTRACTION    BY   ENDINGS. 
1,33.  4  +  4. 

Add: 

4     14    24     34    44    54    64     74     84    94 
4444444444 

Make  a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  4  from  each. 


110       ADDITION  AND  SUBTRACTION  BY  ENDINGS. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

■  212 

444 

929 

424 

394 

793 

444 

943 

393 

492 

834 

339 

422 

222 

994 

333 

919 

449 

244 

779 

933 

629 

343 

333 

444 

322 

243 

333 

424 

934 

422 

988 

928 

837 

233 

382 

244 

232 

933 

292 

392 

893 

444 

424 

397 

486 

398 

329 

243 

787 

683 

766 

629 

829 

937 

347 

677 

226 

552 

458 

134. 

4  +  5. 

• 

Add: 

14  24 

34  44 

54 

64  74 

84  94 

104 

5   5 

5   5 

5 

5   5 

5   5 

5 

Make  a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  5  from  each. 


(1) 

(2) 

(3) 

(4) 

(6) 

(6) 

425 

9 

2 

54 

219 

494 

554 

54 

594 

294 

442 

535 

141 

745 

224 

591 

234 

240 

514 

293 

451 

435 

335 

445 

445 

492 

234 

954 

498 

493 

151 

335 

334 

839 

513 

132 

415 

632 

243 

332 

354 

989 

552 

933 

328 

535 

735 

219 

326 

379 

289 

232 

221 

853 

396 

618 

902 

893 

449 

508 

MULTIPLICATION  AND  DIVISION,  111 

135.  4  +  6. 

Add: 

4     14    24    34    44    54    64    76    84    94    104 

Make  a  subtraction  table,  taking  6  from  each  of  the 
results  of  the  above  addition. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

389 

644 

246 

454 

695 

946 

983 

655 

564 

645 

244 

354 

439 

262 

441 

242 

363 

241 

690 

344 

454 

464 

448 

664 

834 

465 

635 

345 

452 

395 

376 

544 

384 

369 

224 

26 

946 

996 

726 

892 

994 

994 

562 

326 

549 

839 

539 

618 

55 

897 

73 

686 

73 

43 

7 

557 

28 

154 

58 

9 

MULTIPLICATION  AND  DIVISION. 

136.  Copy  and  learn: 

9X9=  81  10X10  =  100  11X11  =  121 

10X9=  90  11X10  =  110  12X11  =  132 

11X9=  99  12X10  =  120  12X12  =  144 
12X9  =  108 

Write  these  with  the  9,  10,  and  11  first. 

Recite  the  division  table  from  the  multiplication  table. 


112  MULTIPLICATION  AND  DIVISION. 

137.  MENTAL  EXERCISE. 

1.  At  9  cents  a  pound,  what  will  12  pounds  of  raisins  cost? 

2.  A  newsboy  makes  10  cents  a  day  by  selling  papers; 
how  much  will  he  earn  in  11  days? 

3.  If  12  grape-fruits  cost  144  cents,  how  much  are  they 
apiece? 

4.  When  eggs  are  selling  at  9  cents  a  dozen,  what  will 
9  dozen  cost? 

5.  A  jeweler  received  in  one  week  $132  for  clocks  which 
were  valued  at  $11  each;  how  many  clocks  did  he  sell? 

6.  A  street-car  makes  a  trip  of  11  miles  in  one  hour;  at 
that  rate,  how  many  miles  will  it  run  in  12  hours? 

7.  12  men  working  together  can  do  a  piece  of  work  in 
9  days ;  in  how  many  days  can  one  man  working  alone  do 
the  same  work? 

8.  How  long  will  it  take  an  excursion  party  to  complete 
a  journey  of  121  miles,  walking  11  miles  a  day? 

9.  12  dozen  foliage  plants  were  used  in  the  border  of  a 
garden  walk;  how  many  plants  were  used? 

10.  At  10  cents  a  yard,  how  many  yards  of  muslin  can 
be  bought  for  $1.20? 

11.  At  12  cents  a  pound,  what  will  9  pounds  of  maple 
sugar  cost? 

12.  Make  problems  for: 

lOx  10  =  100        $11)$121         12  bushels)132  bushels 


11  10 

11 X  9=  99        11  miles)110  miles        12  trees)  108  trees 

10  9 

Note. — Do  this  in  class. 


MULTIPLICATION  AND  DIVISION.  113 

13.  Divide  all  numbers  from  9  to  36  by  9,  naming  each 
undivided  remainder. 

14.  Divide  all  numbers  from  11  to  44  by  11. 

15.  Divide  all  numbers  from  12  to  60  by  12. 

16.  641009187695398205965897083 


17.  541798160708943009685479187 

9 


EXERCISE. 

138.   1.  A  gardener  sold  10  geraniums  for  $1  ;    what 
was  the  value  of  each  plant? 

2.  Robert  spent  |  of  $1  for  a  book;  how  many  cents  did 
he  spend? 

3.  I  paid  $1  for  3  pounds  of  coffee;  how  much  was  it  a 
pound? 

4.  If  4  pounds  of  sugar  cost  25  cents,  what  is  the  cost 
of  one  pound? 

5.  George  had  90  cents  and  spent  to   of  his  money  for 
nails;  how  many  cents  did  he  spend? 

6.  12  miles  is  to  of  my  journey;  what  is  the  whole  dis- 
tance? 

7.  132  pounds  of  prunes  were  packed  in  11  boxes  of 
equal  size;  how  many  pounds  were  put  into  each  box? 

8.  I  paid  12  dollars^  which  was  i  of  my  money,  for  some 
peach  trees;  how  much  money  had  I? 

9.  Carl  says,   ''  If  my  marbles  were   divided  equally 


114  MULTIPLICATION  AND  DIVISION, 

among  12  boys,  each  boy  would  receive   11  marbles/' 
How  many  marbles  has  he? 

10.  One  man  working  alone  can  do  a  piece  of  work  in  132 
days;  in  how  many  days  can  12  men  do  the  same  work? 

11.  A  watch  costs  $90,  and  a  chain  i  as  much;  what  is 
the  value  of  the  chain?    Of  both  watch  and  chain? 

12.  A  farmer  sells  144  bushels  of  potatoes  to  12  cus- 
tomers ;  if  they  are  divided  equally,  how  many  bushels  does 
each  receive? 

13.  Make  problems  for: 

9)90  pounds        9)108  miles       tV  of  $120  =  $12. 
10  pounds  12  miles 

1 1)99  cents         1 1)132  dollars     iV  of  1 10  miles  =  10  miles. 
9  cents  12  dollars 

12)84  cents         12)144  inches      tV  of  $108  =  $9. 
7  cents  12  inches 

Note. — Do  this  in  class. 

CLASS  EXERCISE. 

139.  1.  6)29855217448115692558121854109792352 

2.  6)41909373891581097635338589870093874 

3.  7)5523470092665607315858723102163 

4.  7)433547467495487876969201320134 


MULTIPLICATION  TABLE.  115 


140.  MULTIPLICATION    TABLE. 

1X2=  2               1X3=  3  1X4=  4 

2X2=  4              2X3=  6  2x4=  8 

3X2=  6              3X3=  9  3X4  =  12 

4X2=  8              4X3  =  12  4X4  =  16 

5X2  =  10              5X3  =  15  5X4  =  20 

6X2  =  12               6X3  =  18  6X4  =  24 

7X2  =  14               7X3  =  21  7X4  =  28 

8X2  =  16              8X3  =  24  8X4  =  32 

9X2  =  18              9X3  =  27  9X4  =  36 

10X2  =  20  10X3  =  30  10X4  =  40 

11X2  =  22  11X3  =  33  11X4  =  44 

12X2  =  24  12X3  =  36  12X4  =  48 


1X5=  5  1X6=  6  1X7=  7 

2X5  =  10  2X6  =  12  2X7  =  14 

3X5  =  15  3X6  =  18  3X7  =  21 

4X5  =  20  4X6  =  24  4X7  =  28 

5X5  =  25  5X6  =  30  5X7  =  35 

6X5  =  30  6X6  =  36  6X7  =  42 

7X5  =  35  7X6  =  42  7X7  =  49 

8X5  =  40  8X6  =  48  8X7  =  56 

9X5  =  45  9X6  =  54  9X7  =  63 

10X5  =  50  10X6  =  60  10X7  =  70 

11X5  =  55  11X6  =  66  11X7  =  77 

12X5  =  60  12X6  =  72  12x7  =  84 


116  MULTIPLICATION   TABLE. 

1X8=  8  1X9=     9  1X10=   10 

2X8  =  16  2X9=   18  2x10=  20 

3X8  =  24  3X9=  27  3X10=  30 

4X8  =  32  4X9=  36  4x10=  40 

5X8  =  40  5X9=  45  5X10=  50 

6X8  =  48  6X9=  54  6x10=  60 

7X8  =  56  7X9=  63  7X10=  70 

8X8  =  64  8X9=  72  8X10=  80 

9X8  =  72  9X9=  81  9X10=  90 

10X8  =  80  10X9=  90  10X10  =  100 

11X8  =  88  11X9=  99  11X10  =  110 

12X8  =  96  12X9  =  108  12X10  =  120 

1X11=   11  1X12=   12 

2X11=  22  2X12=  24 

3X11=  33  3X12=  36 

4X11=  44  4X12=  48 

5X11=  55  5X12=  60 

6X11=  66  6X12=  72 

7X11=  77  7X12=  84 

8X11=  88  8X12=  96 

9X11=  99  9X12  =  108 

10X11  =  110  10X12  =  120 

11X11  =  121  11X12  =  132 

12X11  =  132  12X12  =  144 

Be  sure  to  read  these  tables  both  ways. 


CHAPTER  V. 
READING  AND  WRITING  NUMBERS. 
Two  Periods:  Units  and  Thousands. 

2d  period.        Ist  period. 
Thousands.    Units  (ones). 


0   0   0         0   0   0 

141.  Ten  ten-thousands  are  equal  to  one  hundred- 
thousand. 

One  hundred-thousand  is  how  many  times  ten  thousand? 

Hundred-thousands  are  written  in  the  first  place  to  the 
left  of  ten-thousands. 

405,623  is  read,  "  four  hundred  five  thousand  six  hundred 
twenty-three/'  The  figure  4  expresses  the  number  of 
hundred-thousands. 

In  the  number  405,623,  in  what  place,  or  order,  does  the 
figure  6  stand?     The  figure  4?    2?     0? 

Ten  units  of  any  order  make  one  of  the  next  higher  order. 

Expressing  numbers  by  means  of  figures  is  called  Nota- 
tion.    Expressing  numbers  in  words  is  called  Numeration. 

142.  Write  6  ciphers  and  separate  them  into  periods. 
Place  3  in  hundred-thousands'  place,  2  in  thousands'  place, 
and  4  in  hundreds'  place.  Read  the  number  you  have 
written. 


118  READING  AND  WRITING  NUMBERS 

Read  the  following  numbers: 

401,392       500,020       800,005  110,111 

503,001       909,008       850,050  101,001 

648,406       763,204       616,016  111,101 

Express  the  following  in  figures : 
Two  hundred  thousand  sixty-three. 
Seven  hundred  seven  thousand  eighty-one. 
Five  hundred  fifty-one  thousand  one. 
Eight  hundred  eighteen  thousand  six. 
One  hundred  eleven  thousand  eleven. 
Two  hundred  thousand  twelve. 
Nine  hundred  ninteen  thousand  nineteen. 

Three  Periods:  Units,  Thousands,  and  Millions. 

3d  period.        2d  period.        lat  period. 
Millions.       ThouBands.  Units. 


fl«.5       c«.-§       fl«5 

^    S    ^  ^   S    a  S   ^    s 

000         000         000 

143.  The  third  period  of  figures  expresses  ones  of  mil- 
lions, tens  of  millions,  and  hundreds  of  millions. 

Write  9  ciphers  and  separate  them  into  periods.  Place 
3  in  ten-thousands'  place,  6  in  ten-millions'  place,  8  in 
tens'  place,  4  in  thousands'  place,  and  7  in  milUons'  place. 
Read  the  number. 

Read  the  following  numbers: 

100,000,000  150,004,150  19,300,019 

1,000,000  50,040,040  9,999,000 

4,700,630     804,307,321     11,110,011 

20,343,101      10,010,001     10,111,101 


MULTIPLYING  AND  DIVIDING  BY  9,  10,  11,  AND  12.  119 
Write  in  figures: 

Fifty-six  million  one  hundred  seventeen  thousand  six 
hundred  nine. 

Three  hundred  eight  thousand  three  hundred  eight;  six 
million  sixteen. 

Ten  million  one  hundred  eleven  thousand  one. 

MULTIPLYING  AND  DIVIDING  BY  9,  10,  11,  AND  12. 
144.  Multiply  by  9: 

1.  8439        6.    5968      11.    6874      16.    9005       21.    6298 

2.  7095        7.    6374       12.    3758      17.    8161       22.    2759 

3.  6394        8.   4738      13.    8647      18.    7463       23.    8463 


4.  8007 


9.  6834   14.  9376   19.  6389   24.  3874 


5.  6398   10.  4958   15.  4837   20.  8476   25.  6438 


145. 

9-^9  =  0 

10-^9  =  1,  Irem. 
11-9  =  1,  2  rem. 
12-9  =  1,  3  rem. 
13-9  =  1,  2  rem. 
14-9  =  1,  5  rem. 
15-9  =  1,  6  rem. 
16-^9  =  1,  7  rem. 


CLASS    EXERCISE. 

17^9  =  1,  8  rem. 
18^9  =  2 
19-^9  =  2,  Irem. 
20^9  =  2,  2  rem. 
21-9  =  2,  3  rem. 
22-9  =  2,  4  rem. 
23-^9  =  2,  5  rem. 
24-9  =  2,  6  rem. 


25-7-9  =  2,  7  rem. 
26^-9  =  2,8  rem. 
27^9  =  3 
28^9  =  3,  Irem. 
29-^9  =  3,  2  rem. 
30-^9  =  3,  3rem. 
31^9  =  3,  4  rem. 
32-9  =  3,  5  rem. 

Beginning  with  33,  complete  the  table  to  108  -r-  9,  each 
pupil  giving  one  number  divided  by  9. 


Note,— Do  this  in  class. 


120  MULTIPLYING  AND  DIVIDING  BY  9,  10,  11,  AND  12, 

Divide : 

8)39806956597477590077495805479723136 

8)7767000543372858384567121413212 

9)44782826172173538837182781164688528 

9)17343806471078661983608026751009801 

146.  Divide  by  9: 

1.  15443  7.  13540  13.  39128  19.  53080  25.  29123 

2.  17867  8.  44547  14.  29109  20.  44064  26.  20367 

3.  27364  9.  88432  15.  24389  21.  41229  27.  23389 

4.  72351  10.  76302  16.  66093  22.  45562  28.  35198 

5.  11128  11.  68134  17.  75623  23.  89054  29.  55555 

6.  55408  12.  47562  18.  64224  24.  76323  30.  44444 

147.  Multiply: 

1.  7865X10        8079X10         80563X10        96532x10 

Short  Method.  When  the  multiplier  is  ten,  the  product  is 
obtained  by  annexing  zero  to  the  multiplicand. 

2.  89736X10       78895x10       45838X10       40009X10 

Find  quotients : 

3.  28930^10      26845-^10      870470-10      693879^10 

Short  Method.  Cut  oflP  one  figure  from  the  right  of  the  divi- 
dend. The  part  cut  off  is  the  remainder  and  the  rest  of  the 
dividend  is  the  quotient. 

4.  7630456^-10         3987652-10  3101487 -f- 10 


MULTIPLYING  AND  DIVIDING  BY  9,  10, 11,  AND  12.  121 
148.  Multiply  by  11: 


1.  89723 

2.  65049 


3.  830976 

4.  394857 


5.  385047 

6.  629875 


7.  748693 

8.  480019 


149. 


11 
12-1 
13^1 
14-1 


15 


=  1  16 

=  1,1  rem.  17^1 

=  1,2  rem.  18-^1 

=  1,3  rem.  19^1 

=  1,4  rem.  20^1 


MENTAL    EXERCISE. 
1 


=  1,5  rem.  21-11  =  1,  10  rem. 

=  1,6  rem.  22-11=2 

=  1,7  rem.  23-^11=2,  1  rem. 

=  1,8  rem.  24  -11  =2,  2  rem. 

=  1,  9  rem.  25  -11=2,  3  rem. 


Beginning  with  26,  complete  the  table  to  132—11,  each 
pupil  giving  one  number  divided  by  11. 


150.  Divide  by  11: 


1.  25826 

2.  20441 

3.  37838 


4.  899604 

5.  283563 

6.  190009 


7.  567802 

8.  900456 

9.  404040 


10.  9800457 

11.  2394836 

12.  1938479 


151.  Find  the  products: 


1. 
2. 
3. 
4. 


7809X12 
9489X12 
7618X12 
9284X12 

5.  29848X12 

6.  72952X12 

7.  47836X12 

8.  39647X12 


9.  63749X12 

10.  34952X12 

11.  6784X12 

12.  56900X12 

13.  61809X12 

14.  19072X12 

15.  72839X12 

16.  85535X12 


122 


MISCELLANEOUS  PROBLEMS. 


152. 

12-12  =  1 


13 


14-12  =  1,  2  rem. 


16 
17 


12  =  1,  Irem. 


MENTAL    EXERCISE. 

18^12  =  1,    6  rem.    24-12  =  2 

19 

20 


15h-12  =  1,  3rem.    21^12=1,    9  rem.    27 


12  =  1,  4  rem.    22 
12  =  1,  5  rem.    23 


12  =  1,    7  rem.    25 
12  =  1,    8  rem.    26 


12  =  1,  10  rem.    28  h- 12  =  2,  4  rem. 
12  =  1,  11  rem.    29^12  =  2,  5  rem. 


12  =  2,  Irem. 
12  =  2,  2  rem. 
12  =  2,  3  rem. 


Complete  the  table  to  144-12. 


153.  Divide  by  12: 


1.  6384 

2.  2952 

3.  29548 

4.  98345 

5.  54389 

6.  87432 


7.  49673 

8.  83440 

9.  970836 

10.  483974 

11.  298375 

12.  483762 


13.  7864532 

14.  1111111 

15.  9999999 

16.  3568903 

17.  2494967 

18.  8607859 


19.  9860004 

20.  7581924 

21.  9676893 

22.  6892853 

23.  4786900 

24.  6927465 


MISCELLANEOUS  PROBLEMS. 

154.  1.  John  says,  ''  Four  times  my  money  is  $1.00"; 
how  many  cents  has  he? 

2.  What  will  12  pounds  of  soap  cost  at  12  J  cents  a  pound? 

3.  75  cents  is  ^  of  my  money;  how  much  money  have  1? 

4.  What  was  received  in  payment  for  867  desks  sold  at 
$9  each? 

5.  Rugs  which  cost  $7.50  each,  were  sold  for  $8.00 
apiece ;  what  was  the  profit  on  each  rug?     On  12  rugs? 

6.  What  is  the  cost  of  36  bolts  of  ribbon  at  $9  a  bolt, 
and  25  yds.  of  velvet  at  $5  a  yard? 


MISCELLANEOUS  PROBLEMS.  123 

7.  A  merchant  bought  9  pieces  of  merino,  each  piece 
containing  45  yards.  After  selHng  135  yards,  how  many 
dress  patterns  of  9  yards  each  had  he  left? 

8.  A  clerk  saves  $9  a  month;  how  many  months  will 
it  take  him  to  save  $684? 

9.  Bought  882  acres  of  woodland.  After  clearing  one- 
ninth  of  it,  I  sold  the  remainder  at  $9  an  acre;  how  much 
did  I  receive? 

10.  If  you  have  $238  when  you  are  18  years  old,  and  save 
$49  each  year  until  you  are  27,  how  much  money  will  you 
then  have? 

11.  A  lady  having  $125,  bought  a  cloak  for  $75,  and  7 
yards  of  silk  at  $2  a  yard;  how  much  money  had  she  left? 

12.  A  coal-dealer  bought  11  tons  of  coal  for  $126.50  and 
sold  it  at  $12  a  ton;  did  he  gain  or  lose?    How  much? 

13.  A  hotel-keeper  bought  98  pounds  of  crackers  at  8 
cents  a  pound,  and  138  loaves  of  bread  at  4  cents  a  loaf; 
how  much  did  he  pay  for  both? 

14.  At  5  cents  a  quart,  what  is  the  value  of  a  barrel  of 
cider  containing  31^  gallons? 

15.  A  manufacturer  received  $2688  for  gloves,  at  the  rate 
of  $12  per  dozen  pairs;  how  many  dozen  pairs  did  he  sell  ? 

16.  How  many  days  are  there  in  eleven  years? 

17.  A  shoe  merchant  received  $288  for  12  dozen  pairs  of 
shoes;  what  was  the  value  of  one  dozen  pairs?  Of  one 
pair? 

18.  $37,863  were  received  in  three  months  for  coal  sold 
at  $9  a  ton;  how  many  tons  were  sold? 

19.  An  office  building  valued  at  $600,000  is  owned  by  a 
company  of  12  men;  the  rental  received  each  year  is 
$30,000.     What  is  each  man's  share  of  the  rent? 


124      ADDITION  AND  SUBTRACTION   BY   ENDINGS. 

20.  How  many  barrels  of  flour,  at  $9  per  barrel,  will  pay 
for  60  cords  of  wood,  at  $12  per  cord? 

21.  12  men  can  do  a  piece  of  work  in  20  weeks;  in  how 
many  weeks  can  one  man  do  the  same  work? 

22.  How  many  revolutions  will  be  made  by  a  wheel  12 
feet  in  circumference  in  running  52,800  feet? 


ADDITION  AND   SUBTRACTION   BY  ENDINGS. 

155.  4  +  7. 

Add: 

4     14    24    34    44    54    64    74    84    94 

Make  a  subtraction  table,  taking  7  from  each  of  the 
results  of  the  above  addition. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

634 

646 

689 

956 

497 

90 

476 

443 

344 

734 

973 

994 

634 

574 

765 

275 

748 

427 

446 

437 

337 

347 

480 

99 

667 

649 

784 

564 

39 

749 

743 

767 

369 

449 

3 

969 

367 

424 

244 

992 

989 

793 

473 

396 

936 

738 

927 

739 

452 

787 

879 

788 

697 

77 

849 

567 

652 

253 

47 

64 

7.  477 + 743 + 267 + 344  +  598  +  442  +  675  +  484  +  834  + 
646=? 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.      125 

8.  Add  594,  764,  432,  474,  544,  347,  854,  334,  788,  and 
568. 

9.  Find  the  amount  of  9,  93,  838,  297,  944,  469,  93,  739, 
479,  and  60. 

10.  Find  the  sum  of  9,  34,  897,  378,  949,  983,  639,  84, 1, 
78,  and  78. 

11.  44  +  987  +  909  +  738  +  493  +  989  +  37  +  704  +  989  +  44 
+  7=? 

12.  839  +  799  +  3  +  488  +  937  +  784  +  478  +  842  +  649  +  83 
+9+9=? 

13.  Add  39,  899,  980,  97,  734,  97,  473,  648,  783,  68,  4,  7. 

REVIEW. 

156.  Add    rapidly,  giving    the    ending   figures    first, 
then  the  whole  sum: 

69785979 
22        32        42        52        62        72        82        92 


9 

8 

7 

6 

9 

7 

8 

9 

23 

33 

43 

53 

63 

73 

83 

93 

5 

4 

6 

7 

5 

7 

6 

7 

24 

.34 

44 

54 

64 

74 

84 

94 

4 

4 

4 

4' 

4 

4 

4 

4 

34 

46 

55 

67 

74 

85 

95 

37 

Add  the  following  lines,  beginning  at  the  left: 

7,  7,  4,  2,  4,  4,  2,  5,  4,  1,  4,  5,  1,  5,  3,  3,  3. 

8,  8,  4,  6,  4,  4,  4,  2,  5,  4,  1,  5,  4,  2,  8,  3,  2,  9. 


126      ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

5,  4,  4,  9,  8,  4,  5,  1,  4,  4,  2,  9,  3,  7,  2,  3,  6,  4. 

7,  4,  5,  4,  7,  4,  7,  3,  3,  6,  5,  4,  1,  9,  3,  2,  6,  7. 

8,  3,  7,  3,  4,  4,  2,  8,  3,  3,  4,  3,  8,  7,  4,  8,  3,  2. 

9,  3,  9,  9,  8,  3,  7,  3,  6,  4,  4,  4,  1,  7,  4,  5,  4,  9. 

157.  4  +  8. 

4    14    24    34    44    54    64    74    84    94    104 

8888888888        8 

Make  a  subtraction  table,  taking  8  from  each  of  the 
results  of  the  above  addition. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

448 

283 

184 

444 

979 

89 

662 

224 

626 

666 

887 

48 

448 

484 

484 

444 

222 

994 

662 

644 

226 

636 

348 

479 

848 

882 

484 

433 

563 

749 

262 

244 

826 

447 

387 

984 

448 

866 

284 

384 

744 

936 

880 

288 

841 

327 

399 

994 

526 

447 

28 

773 

393 

649 

38 

267 

939 

668 

968 

99 

7.  Add  384,  384,  348,  314,  958,  328,  733,  493,  889,  and 
269. 

8.  Find  the  sum  of  799,  423,  853,  124,  489,  534,  928,  298, 
988,  and  464. 

9.  84+47  +  978+288  +  784  +  349  +  899+892  +  699  +  34  + 
48  +  84=  ? 

10.  Find  the  amount  of  83,  387,  938,  974,  949,  889,  398, 
794,  448,  983,  348,  87,  4. 


ADDITION  AND  SUBTRACTION  BY  ENDINGS, 


127 


158.  Subtract: 

1.  2442-2546 

2.  13123-1666 

3.  43454-1456 

4.  23455-1666 

5.  35656-4666 

6.  60003-2666 


7.  53320-1777 

8.  44320-2676 

9.  39131-7777 

10.  68442-6767 

11.  49563-6777 

12.  18004-7777 


13.  37404-6476 

14.  18805-3076 

15.  99405-6066 

16.  97503-6707 

17.  19505-6007 

18.  13006-1007 


MISCELLANEOUS  PROBLEMS. 

159.  1.  Two  numbers,  taken  together,  make  1000. 
One  of  the  numbers  is  320;  what  is  the  other  number? 

2.  Find  the  difference  between  534  and  3034. 

3.  Subtract  12  from  1000. 

4.  An  excursion  train  left  Chicago  for  Niagara  Falls  with 
543  passengers.  On  the  way  254  passengers  left  the  cars 
and  162  came  aboard;  how  many  were  on  the  train  when 
it  reached  Niagara  Falls? 

5.  Morris  paid  50  cents  for  a  hammer,  $1.25  for  a  saw, 
75  cents  for  a  file,  25  cents  for  a  gimlet,  25  cents  for  a  screw- 
driver, $1  for  an  auger,  50  cents  for  a  chisel,  and  $2  for  a 
plane;  how  much  did  his  tools  cost  him? 

6.  If  he  should  sell  his  tools  for  $6,  would  he  gain  or 
lose?     How  much? 

7.  The  sum  of  3  numbers  is  1345.  Two  of  the  numbers 
are  300  and  400;  what  is  the  third? 

8.  From  a  cask  containing  900  gallons  of  kerosene  I  sold 
at  different  times  200  gallons,  165  gallons,  and  150  gallons; 
how  many  gallons  remained  in  the  cask? 


128  MULTIPLICATION. 

9.  A  gentleman  bought  a  lOOO-mile  ticket  on  a  railroad 
for  the  use  of  his  wife,  his  daughter,  his  son,  and  himself. 
His  wife  rode  233  miles,  his  daughter  289  miles,  his  son 
221,  and  he  himself  rode  the  remainder;  how  many  miles 
did  he  ride? 

10.  A  farmer  raised  225  bushels  of  blue-grass  seed.  He 
sowed  74  bushels,  and  sold  95  bushels;  how  many  bushels 
had  he  left? 

11.  A  has  $629,  B  has  $865,  C  has  $786,  and  D  has  as 
much  as  A,  B,  and  C;  how  many  dollars  has  D? 

12.  A  has  $2400,  B  has  $500  less  than  A,  C  has  $150  less 
than  B;  how  much  money  has  C? 

MULTIPLICATION. 

When  the  Multiplier  Consists  of  More  Than  One  Order. 

160.  Multiply  234  by  25. 

234  (multiplicand)       (1)  234  units  multiplied  by 

25  (multiplier)       5-1170  uuits. 

(2)  234   units   multiplied  by 

5  times  234  =1170  2  tens    (or  20)  =  468    tens,    or 

20  times  234  =  468  4680  units.     The  8  tens  in  this 

or  x-  oo^      ror/^  ,      ,    ..        product    are   written    in    tens' 

25  times  234  =  5850  (product)       ^         ..u    ^  u     j    j    •     u 

place,  the  6  hundreds  in  hun- 
dreds' place,  and  the  four  thousands  in  thousands'  place.     (It  is 
not  necessary  to  write  the  zero  as  the  right  hand  figure  of  this 
product,  as  8  tens  means  80  units.) 
(3)  1170  +  4680  =5850. 

Note. — The  process  of  multiplication  may  be  taught  as  given 
above  without  further  explanation.  If  it  is  thought  best  to  make 
a  more  extended  study  of  the  process,  the  following  method  may 
be  useful : 


UNITED  STATES  MONEY.  129 


5  times  234 

=  1170  (Ist  partial  product) 

20  times     4 

=     80^ 

20  times     3  tens 

=  600  [ 

20  times      2  hundreds; 

=4000  ' 

4680  (2<1  partial  product) 

1170  +  4680  = 

=  5850  (product). 

Find  products: 

1. 

4697X26 

13. 

1086X97 

2. 

8309X28 

14. 

8594X85 

3. 

3597X34 

15. 

9457X69 

4. 

4318X28 

16. 

3749X58 

5. 

7906X47 

17. 

4008X37 

6. 

6708X39 

18. 

8096X59 

7. 

8009X95 

19. 

9085X68 

8. 

7926X87 

20. 

6927X74 

9. 

0193X68 

21. 

9619X47 

10. 

9658X76 

22. 

6538X87 

11. 

9037X98 

23. 

7108X98 

12. 

8395X79 

24. 

8693X80 

In  example  24,  multiply  by  8  and  annex  one  cipher. 

UNITED  STATES  MONEY. 

161.     Read  the  following: 

$426.37  $4003.90  $50035.05 

$200.02  $9040.09  $16200.15 

$187.07  $1919.19  $70017.17 

Express  in  figures: 

Nine  hundred  sixty-seven  dollars  eight  cents. 

Fifty-two  thousand  eleven  dollars  seven  cents. 


130  UNITED  STATES  MONEY 

Forty-one  thousand  eleven  dollars  seven  cents. 
Eleven  thousand  one  hundred  dollars  one  cent. 

What  will  4  barrels  of  flour  cost,  at  $6.80  a  barrel? 

$6.80,  cost  of  one  barrel. 
4 


$27.20,  cost  of  4  barrels. 

Multiply  as  in  simple  numbers,  and  if  there  are  cents  in  the 
multiplicand,  point  off  two  places  for  cents  in  the  product. 

Find  products : 

1.  $16.15X3  4.  $286.04X3  7.  $0.89x4 

2.  $26.10X2  5.  $480.70X4  8.  $0.75X3 

3.  $45.01X5  6.      $0.85X5  9.  $0.90X5 

Multiply: 

10.  $9.50  by  48   13.  $8.72  by  75   16.  $16.87  by  68 

11.  $10.54  by  36   14.  $7.96  by  87   17.  $20.35  by  95 

12.  $12.54  by  65   15.  $11.84  by  96   18.  $35.62  by  76 

EXERCISE. 

163.  1.  There  are  24  rows  of  trees  in  an  orchard  and 
196  trees  in  each  row;  how  many  trees  does  it  contain? 

2.  There  are  24  hours  in  a  day;  how  many  hours  are 
there  in  a  year? 

3.  If  a  ton  of  coal  costs  $9.75,  what  must  I  pay  for 
95  tons  ? 

4.  If  there  are  78  school  buildings  in  a  city  and  an  average 
of  690  pupils  in  each  building,  how  many  pupils  are  there 
in  all  the  schools  of  the  city? 

5.  There  are  144  pens  in  a  box;  how  many  pens  are 
there  in  75  boxes? 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.      131 

6.  If  flour  is  selling  at  $5.75  a  barrel,  what  is  the  value 
of  85  barrels? 

7.  A  man  earns  $175  a  month;  how  much  does  he  earn 
in  3  years? 

8.  If  there  are  196  pounds  of  flour  in  a  barrel,  how  many 
pounds  do  65  barrels  contain? 

9.  Albert  earns  $10.50  a  week;  how  much  does  he  earn 
in  a  year? 

10.  There  are  5280  feet  in  a  mile;  how  many  feet  are 
there  in  98  miles? 

ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

163.  4  +  9. 

Add: 

4     14    24    34    44    54    64    74    84    94     104 
9999999999        9 


Make  a  subtraction  table,  taking  9  from  each  of  the 
results  of  the  above  addition. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

422 

222 

499 

998 

979 

694 

649 

494 

911 

499 

943 

948 

961 

616 

144 

794 

468 

498 

199 

949 

966 

948 

797 

989 

311 

161 

149 

497 

343 

894 

449 

494 

941 

979 

879 

347 

261 

616 

124 

994 

698 

984 

994 

949 

943 

649 

44 

498 

444 

337 

228 

47 

9 

43 

565 

717 

828 

4 

50 

38 

132      ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

7.  Add  98,  949,  899,  981,  444,  96,  974,  443,  78,  and  68. 

8.  Find  the  amount  of  949,  377,  994,  899,  448,  79,  794, 
948,  98,  and  744. 

9.  Find  the  sum  of  998,  874,  949,  467,  94,  848,  78,  894, 
749,  87,  44,  and  9. 

10.  78+90+949+478+44  +  909  +  887+94+989+708+ 
79+3  =  ? 

11.  84+939+47+874+478+848+869  +  44  +  989  +  787 
+  44  +  20=? 

12.  44+969+448+99+794+447  +  74+878+849+94+ 
49+489=? 


164.  Subtract: 

1. 

24321- 

2878 

18. 

39705- 

16706 

2. 

16653- 

388 

19. 

10000- 

6117 

3. 

37304- 

5888 

20. 

69676- 

5767 

4. 

48765- 

4878 

21. 

49075- 

7076 

5. 

29530- 

4878 

22. 

29640- 

6777 

6. 

14878- 

7807 

23. 

90653- 

3767 

7. 

88676- 

17878 

24. 

20412- 

7777 

8. 

19644- 

888 

25. 

10586- 

5767 

9. 

20595- 

5468 

26. 

70001- 

4006 

10. 

60677- 

6878 

27. 

80076- 

2076 

11. 

69004- 

10768 

28. 

70604- 

5075 

12. 

78002- 

7834 

29. 

60243- 

4767 

13. 

44320- 

1667 

30. 

59456- 

7537 

14. 

36543- 

4757 

31. 

17653- 

2767 

15. 

17654- 

5667 

32. 

69114- 

7116 

16. 

28065- 

6776 

33. 

80000- 

67 

17. 

38345- 

14677 

34. 

91011- 

8927 

ADDITION  AND  SUBTRACTION.  133 

EXERCISE. 

165.  1.  A  man  bought  a  coat  for  $24,  a  hat  for  $5, 
a  pair  of  shoes  for  $6,  and  a  cravat  for  $1.50;  how  much  did 
they  all  cost? 

2.  I  give  a  fifty-dollar  bill  in  paying  an  account  of  $36.37; 
how  much  change  should  I  get? 

3.  The  difference  between  two  numbers  is  1160.  The 
smaller  number  is  8340;  what  is  the  larger  number? 

4.  Washington  was  born  in  1732;  in  what  year  was  he  57 
years  old? 

5.  260  bushels  of  potatoes  is  55  bushels  more  than  a 
grocer  sold  during  the  month  of  September;  how  many 
bushels  did  he  sell? 

6.  Bought  30  yards  of  cloth  for  $96.90,  20  yards  of  carpet 
for  $40,  and  two  pairs  of  curtains  for  $16.50;  what  did  all 
cost? 

7.  Bought  a  farm  for  $13716,  and  sold  it  for  $13379;  did 
I  gain  or  lose?     How  much? 

8.  A  saleswoman  earns  $0.89  a  day,  and  her  expenses  are 
$3.75  a  week;  how  much  does  she  save  in  a  week? 

9.  I  bought  a  house  for  $6500,  spent  $1876  in  improve- 
ments, and  then  sold  it  for  $9155;  how  much  did  I  gain? 

10.  Of  a  railroad  2465  miles  long,  1266  miles  are  double 
track;  how  many  miles  are  single  track? 

MENTAL    EXERCISE. 

166.  1.  How  many  days  are  there  in  9  weeks? 

2.  How  many  six-inch  pencils  can  you  cut  from  54  inches 
of  lead? 


134  MENTAL  EXERCISE. 

3.  The  minute  hand  goes  round  the  dial  in  an  hour; 
how  many  minutes  is  it  in  passing  over  iV  of  this  space? 

4.  A  confectioner  put  up  52  pounds  of  candy  in  8  boxes 
of  equal  size;  how  many  pounds  did  each  box  contain? 

5.  The  water  in  a  tank  is  72  inches  deep;  how  many  feet 
deep  is  it? 

6.  7^  pecks  of  beans  are  how  many  quarts? 

7.  Bessie  had  54  cents;  she  spent  9  cents  for  envelopes. 
The  remainder  of  her  money  will  pay  for  how  many  street- 
car rides,  if  she  pays  5  cents  each  time? 

8.  A  farmer  having  56  bushels  of  potatoes,  planted  \  of 
them  ;  how  many  bushels  did  he  plant  ?  How  many 
pecks  ? 

9.  Frank  had  70  cents;  he  spent  4"  of  it  for  a  ball  of 
twine,  4  for  some  nails,  and  with  the  remainder  he  bought  a 
Reader;  what  did  his  Reader  cost? 

10.  If  a  cook  uses  6  eggs  each  day,  how  many  days  will  8 
dozen  last? 

11.  How  many  sides  have  two  triangles?  How  many 
plants  will  be  needed  for  two  triangular  garden  plats,  if  9 
are  planted  on  each  side?     (Make  a  drawing.) 

12.  If  a  man  works  at  his  trade  nine  hours  a  day,  how 
many  hours  does  he  work  in  a  week? 

13.  16  bushels  of  oats  are  how  many  pecks? 

14.  I  bought  eight  yards  of  muslin  at  7  cents  a  yard,  and 
gave  in  payment  a  fifty-cent  piece  and  a  ten-cent  piece; 
what  change  ought  I  to  receive? 

15.  At  the  rate  of  72  pages  in  7  days,  how  many  pages  do 
I  read  in  a  day? 

16.  Ten  cents,  which  Horace  paid  for  his  drawing  book, 
was  one-eighth  of  his  money;  how  much  had  he? 


HALVES,    THIRDS,  AND  SIXTHS. 


135 


17.  A  florist  having  7  dozen  roses,  sold  one-fourth  of 
them;  how  many  did  he  sell? 

18.  If  a  peck  of  berries  costs  96  cents,  how  much  are  they 
a  quart? 

19.  If  you  have  collected  8  dozen  stamps,  of  which  I  are 
6-cent  stamps,  how  many  6-cent  stamps  have  you? 

20.  If  5  cents  is  paid  for  a  cup  of  coffee,  4  cents  for  fish, 
and  2  cents  for  bread,  what  will  6  such  breakfasts  cost? 

21.  If  I  earn  54  dollars  a  month,  and  save  }  of  it,  in  how 
many  months  will  I  save  72  dollars? 

22.  How  many  inches  are  there  in  8  feet? 

23.  6  dozen  rosebuds  will  be  enough  for  how  many 
bouquets,  if  9  are  used  for  each  one? 

24.  I  bought  2  yards  of  flannel  for  75  cents;  what  was  the 
cost  of  1  yard? 

25.  If  96  tiles  are  used  for  a  fireplace,  how  many  dozen 
are  used? 

HALVES,  THIRDS,  AND  SIXTHS. 


Note. — Use  objects  freely  in  work  with  fractions. 

16 7.  1.  One  third  of  an  orange  is  equal  to  how  many 
sixths? 


136  HALVES,   THIRDS,  AND  SIXTHS. 

2.  One  half  is  how  many  sixths? 

3.  Fold  a  square  of  paper  into  two  equal  oblongs;  one  of 
the  oblongs  is  what  part  of  the  whole? 

4.  Measure  and  draw  (parallel  to  the  line  made  by  fold- 
ing) lines  which  shall  divide  the  paper  square  into  three 
equal  oblongs  One  of  these  oblongs,  made  by  drawing,  is 
what  part  of  the  whole  square? 

5.  How  does  one  of  these  oblongs  compare  in  size  with  J 
the  square?    Which  is  larger  J  or  J? 

6.  A  third  and  half  of  a  third  will  make  what  part  of  the 
whole  square? 

7.  Fold  your  square  into  six  equal  oblongs.  One  of  the 
oblongs  is  what  part  of  the  whole  square? 

8.  I  are  what  part  of  the  whole?  J  is  equal  to  how  many 
sixths? 

9.  I  are  what  part  of  the  whole? 

10.  Take  away  J  of  the  square;  how  many  sixths  are 
left? 

168.  1.  Draw  an  oblong  on  your  slate;  divide  it  into 
six  equal  oblongs.     One  of  these  is  what  part  of  the  whole? 

2.  Three  of  the  small  oblongs  are  what  part  of  the  large 
one? 

From  your  drawing  find  the  answers  to  these  questions: 

3.  ^  and  }  are  how  many  sixths? 

4.  I  +  J  are  how  many  sixths? 

5.  i  + J  are  how  many  sixths? 


6. 

*+4=?  10. 

i  +  i=?   14. 

|-^=? 

18. 

t-J=? 

7. 

l+i=?  11. 

4  +  f=?   15. 

f-4  =  ? 

19. 

*-*=? 

8. 

*  +  §  =  ?   12. 

f  +  i=?   16. 

?-J  =  ? 

20. 

!-§=? 

9. 

4Xi  =  ?   13. 

3Xi=?   17. 

6Xi  =  ? 

21. 

3X|  =  ? 

HALVES,   THIRDS,  AND  SIXTHS.  137 

22.  i  are  how  many  thirds? 

23.  I  are  how  many  halves? 

24.  f  are  how  many  thirds? 

169.  1.  A  grocer  bought  a  cheese,  of  which  he  sold 
i  on  Monday,  and  J  on  Tuesday;  what  part  of  the  whole 
cheese  remained  unsold? 

2.  Henry  is  24  miles  from  home.  In  returning,  he  rides 
J  of  the  distance  on  his  bicycle,  |  on  horseback,  and  walks 
the  remainder;  how  many  miles  does  he  walk? 

3.  12  cents  is  half  my  money;  how  many  cents  have  I? 
Two  times  the  half  of  anything  equals  what? 

4.  6  cents  is  J  of  EUa^s  money;  how  many  cents  has  she? 
3  times  J  equals  what? 

5.  Find  J  of  2.  Take  two  squares.  Fold  each  into  three 
equal  oblongs.  Divide  these  two  squares  equally  among 
three  children.     One  child  receives  what  part  of  the  whole? 

6.  Place  the  oblongs  so  as  to  form  the  two  squares  again^ 
and  find  the  answers  to  these  questions :  J  of  2  squares  is 
what  part  of  one  square?     J  of  2  is  what  part  of  1? 

7.  i  of  2  cakes  is  what  part  of  one  cake?  J  of  2  pine- 
apples is  what  part  of  1  pineapple? 

8.  Divide  2  pies  equally  among  three  visitors;  how  much 
will  each  receive?     (Picture.) 

170.  Learn  the  following  table: 

i  of  10  =  2  1  of  25  =  121  iofl00  =  33i 

i  of  10  =  21  iof25=  6i  fofl00  =  66f 

iofl0  =  3i  iof50  =  12i  iofl00  =  12i 

f  of  10  =  61  |of50  =  37i  TVoflOO=  8J 

i  of  100  =  161 


CHAPTER  VI. 
MULTIPLICATION  AND  DIVISION. 

ni.  Long  Division. 

Divide  2688  by  12. 

The  process  of  Long  Division  is  the 

Short  Method  same  as  that  of  Short  Division,  exeept- 

i"&  ^^^^  ^^®  w^ork  is  written  in  full. 
12  )  2ooo 

224  (quotient)  ^^^^  contains  12,  two  hundred  times, 

with  2  hundreds  remaining  undivided. 

28  tens  contiiiiis  12,  two  tens  times 

Long  Method.  ^^o  times),  with  4  tens  remaining  un- 

12  )  2688  (  224  (quotient)    divided. 

24  48  units  contains  12,  four  times.     The 

— —  result  is    200  +  20  +  4  =  224. 

24  12)2688(200; 

^^^  2400      20}  =  224 

4^  288 

48  240 

48 
48 


00  J 
20  [: 

4^ 


EXERCISE. 

172.  Divide  the  following  numbers  by  21: 

Use  the  left  hand  figure  of  the  divisor  as  the  trial  divisor. 

1.  672       5.  961  9.  9266 

2.  655       6.  8862  10.  7654 

3.  483       7.  6552  11.  9794 

4.  252       8.  7205  12.  8319 


MULTIPLICATION  AND  DIVISION. 


139 


13.  2043 

14.  3791 

15.  8359 

16.  2043 

17.  7482 

18.  6944 

19.  8752 

20.  9342 

21.  3484 

22.  5184 

23.  1249 

24.  1988 


25.  6732 

26.  8493 

27.  3048 

28.  8065 

29.  9271 

30.  1839 

31.  1692 

32.  9437 

33.  8874 

34.  1986 

35.  2016 

36.  2019 


37.  2026 

38.  9032 

39.  4876 

40.  7654 

41.  5437 

42.  3999 

43.  8763 

44.  4472 

45.  9652 

46.  3698 

47.  4271 

48.  2039 


EXERCISE. 

173.  Divide  32019  by  31. 
31 )  32019  ( 1032 


31 


101 
93 


89 
62 

27  rem. 


Tlie  divisor  is  not  contained  in  the  second 
partial  dividend.  Write  zero  in  the  quotient 
and  annex  the  next  fig-ure  of  tlie  dividend, 
which  gives  the  jmrtial  dividend  101. 


Divide  the  following  numbers  by  31 : 


1.  33065 

2.  34139 

3.  32098 

4.  34129 

5.  34149 

6.  34108 

7.  36128 

8.  30192 


9.  30298 

10.  30179 

11.  30421 

12.  30568 

13.  30671 

14.  30897 

15.  30086 

16.  31008 


17.  18297 

18.  28269 

19.  19134 

20.  17698 

21.  15982 

22.  25769 

23.  22109 

24.  19987 


25.  20081 

26.  30109 

27.  41006 

28.  50963 

29.  81900 

30.  90191 

31.  20018 

32.  11009 


140 


MULTIPLICATION  AND  DIVISION. 


EXERCISE. 

174.  Find  products: 

1. 

3845X64 

17. 

9106X78 

2. 

2762X85 

18. 

8009X41 

3. 

9381X36 

19. 

5970X93 

4. 

7469X94 

20. 

6715X28 

5. 

8309X87 

21. 

8510X99 

6. 

7670X98 

22. 

9296X70 

7. 

9875X36 

23. 

5438X51 

8. 

4319X71 

24. 

2914X98 

9. 

3007X69 

25. 

9009X76 

10. 

6219X92 

26. 

6597X98 

11. 

6101X76 

27. 

7850X49 

12. 

1990X81 

28. 

9687X19 

13. 

9799X19 

29. 

4896X87 

14. 

8423X84 

30. 

8910X93 

15. 

1906X65 

31. 

9768X95 

16. 

7254X37 

32. 

8007X97 

EXERCISE. 

175.  Divide  by  21: 

1.  15960   4.  13242    7.  64692    10.  13455 

2.  17640    5.  10933    8.  147856    11.  9879 

3.  9898    6.  12790    9.  190274    12.  14291 


Divide  by  31 : 

13.  23584    16.  14287 

14.  21405    17.  29159 

15.  15207    18.  21407 


19.  281170   22.  279930 

20.  187240   23.  218567 

21.  126520   24.  188815 


MULTIPLICATION  AND  DIVISION. 


141 


Divide  by  41 : 

25.  31529 

26.  38800 


Divide  by  51 : 

35.  34578 

36.  43163 


27.  28059 

28.  32570 


31.  370667 

32.  388001 


37.  47655 

38.  38175 


41.  19357 

42.  46217 


29.  34826 

30.  249690 


33.  94826 

34.  149690 


39.  35565 

40.  25319 


43.  34704 

44.  360060 


EXERCISE. 

176.  Divide  by  24: 

1.  8747  4.  15571  7.  19384  10.  18975   13.  19678 

2.  30313  5.  23225  8.  8897  11.  97697   14.  89394 

3.  17712  6.  18456  9.  22580  12.  8758   15.  75639 


Divide  by  34: 

16.  26735 

17.  25475 


18.  29165 

19.  20266 


22.  26746 

23.  26887 


20.  33082 

21.  28807 


24.  28943 

25.  86742 


EXERCISE. 

177.  1.  At  $21  an  acre,  how  many  acres  of  land  can  be 
purchased  for  $5187? 

2.  What  will  1296  acres  of  land  cost  at  $45  an  acre? 


142       ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

3.  If  a  man  earns  $24  a  week,  in  how  many  weeks  can  he 
earn  $1248? 

4.  What  is  the  cost  of  9560  pounds  of  butter,  bought  by 
a  commission  house,  at  18  cents  per  pound? 

5.  Mr.  A  spent  $1464  for  trees  at  $24  a  dozen;  how  many 
dozen  did  he  buy? 

6.  If  a  man  saves  $31  a  month,  in  how  many  months  can 
he  save  $1488? 

7.  What  is  the  value  of  950  bushels  of  tomatoes  at  70 
cents  I3er  bushel? 

8.  If  I  travel  at  the  rate  of  35  miles  an  hour,  in  how  many 
hours  can  I  complete  a  journey  of  1225  miles? 

9.  A  commission  house  sold  2980  bushels  of  potatoes  at  65 
cents  per  bushel;  what  was  the  amount  of  money  received? 

10.  45  feet  is  the  width  of  a  lot,  valued  at  85  dollars  per 
foot;  what  is  the  value  of  the  lot? 

11.  The  multipUcand  is  964;  the  multiplier  is  98;  what 
is  the  product? 

12.  The  product  is  9867480;  the  multiplier  is  95;  what 
is  the  multiplicand? 

13.  The  divisor  is  95;  the  quotient  is  9684;  what  is  the 
dividend? 

14.  The  dividend  is  1667120;  the  quotient  is  65;  what 
is  the  divisor? 

ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

ms.  5  +  6  and  5  +  6. 

Add 


5 

15    25 

35 

45 

55 

65 

75 

85 

95 

5 

5      5 

5 

5 

5 

5 

5 

5 

5 

ADDITION  AND  SUBTRACTION  BY  ENDINGS.       143 

5  15     25     35    45     55     65     75     85     95 

6  6      6_^_^_^_^_^_^_^ 

Make  a  table,  subtracting  5  from  each  of  the  results 
above.     Subtract  6  from  the  same  numbers. 


'  (1) 

(2) 

(3) 

(4) 

(5) 

(6) 

536 

266 

694 

594 

598 

964 

554 

544 

557 

692 

657 

798 

656 

556 

654 

887 

454 

457 

455 

654 

265 

446 

559 

754 

561 

465 

725 

95 

656 

489 

543 

545 

645 

769 

982 

835 

655 

556 

565 

625 

694 

496 

445 

634 

42 

843 

848 

758 

644 

426 

487 

89 

87 

458 

142 

665 

67 

64 

74 

54 

Add: 

7.  444,  788,  656,  565,  989,  936,  482,  744,  568,  7,  54. 

8.  99,  459,  855,  595,  644,  976,  65,  626,  848,  89,  53. 

9.  75,  896,  559,  60,  969,  982,  444,  688,  655,  57,  859. 
10.  458,  764,  997,  456,  762,  534,  678,  745,  756,  57,  3. 

179.  5  +  7. 

Add: 

5    15    25    35    45    55    65    75    85    95 

2     1    1    J.    1.    1     111     1 

Make  a  subtraction  table,  taking  7  from  each  of  the 
results  of  the  above  addition. 


144      ADDITION  AND  SUBTRACTION  BY  ENDINGS. 


Add: 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

567 

312 

553 

469 

495 

354 

537 

735 

525 

795 

898 

557 

753 

375 

735 

986 

975 

585 

355 

535 

355 

748 

756 

526 

757 

557 

755 

275 

389 

959 

373 

753 

335 

475 

75 

147 

535 

377 

555 

855 

726 

743 

555 

533 

651 

581 

847 

494 

583 

876 

958 

68 

87 

299 

254 

516 

778 

8 

57 

359 

Add: 

7.  789,  572,  757,  484,  979,  834,  548,  674,  668,  898. 

8.  457,  756,  973,  724,  596,  745,  485,  839,  679,  74. 

9.  479,  620,  799,  239,  497,  775,  48,  797,  872,  99,  4. 

10.  79,  20,  745,  284,  497,  872,  954,  787,  844,  79,  59. 

11.  975,  726,  548,  875,  775,  239,  443,  878,  797,  775,  90. 

180.  B  +  8. 

Add: 

5    15    25    35    45    55    65    75    85    95 

Make  a  subtraction  table,  taking  8  from  each  of  the 
results  of  the  above  addition. 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.       145 


Add: 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

325 

225 

455 

799 

297 

589 

855 

555 

555 

578 

855 

898 

255 

255 

385 

888 

485 

942 

558 

355 

225 

55 

874 

984 

452 

835 

555 

988 

447 

978 

855 

225 

555 

499 

869 

429 

225 

855 

865 

955 

88 

857 

558 

555 

201 

447 

652 

542 

852 

353 

555 

75 

785 

89 

543 

345 

437 

6 

68 

4 

Add: 

7.  979,  944,  577,  647,  962,  875,  225,  848,  2,  88,  955. 

8.  945,  973,  878,  223,  755,  274,  855,  955,  84,  89. 

9.  475,  647,  779,  247,  362,  875,  57,  878,  585,  89,  9. 

10.  75  +  426  +  858  +  962  +  289  +  528  +  872  +  824  +  648  + 
87  +  54=? 

Find  the  sum  of: 

11.  859,  354,  46,  975,  98,  887,  25,  997,  79,  8,  4. 

12.  789,  290,  459,  878,  782,  437,  894,  53,  607,  6,  5. 

MENTAL    EXERCISE. 

181.  1.  If  4  pounds  of  chocolate  cost  50  cents,  how 
many  cents  is  it  a  pound? 

2.  If  a  man  travels  15  miles  in  3  hours,  how  far  will  he 
travel  in  one  hour?     In  9  hours? 

3.  How  many  ounces  are  there  in  a  pound?     What  will 
I  of  a  pound  of  candy  cost,  at  3  cents  an  ounce? 


146  MENTAL  EXERCISE. 

4.  Bought  i  bushel  of  apples  and  ^  bushel  of  peaches; 
what  part  of  a  bushel  have  I?  % 

5.  Bought  4f  pounds  of  grapes  at  6  cents  a  pound;  how 
^uch  did  they  cost? 

6.  If  3  pounds  of  almonds  cost  25  cents,  what  will  one 
pound  cost?    What  will  5  pounds  cost,  at  the  same  rate? 

7.  A  boy  gave  to  his  sister  ^  of  an  orange,  and  to  his 
brother  ^  as  much  as  he  gave  to  his  sister;  how  much  did 
he  give  to  his  sister? 

8.  If  two  pounds  of  cheese  cost  36  cents,  what  will 
1  pound  cost?    What  will  half  a  pound  cost? 

9.  A  bushel  of  corn  weighs  56  pounds ;  what  is  the  weight 
of  a  peck?  a  half  peck? 

10.  A  boy  living  J  of  a  mile  from  school,  who  goes  home 
to  dinner,  will  walk  how  many  miles  each  week  in  going  to 
and  from  school? 

11.  Buy  4  dozen  pencils  at  30  cents  a  dozen,  and  sell 
them  at  4  cents  apiece;  what  is  gained? 

12.  With  what  you  have  gained,  buy  2  dozen  erasers  and 
sell  them  at  6  cents  apiece;  how  much  do  you  gain  this 
time,  and  how  much  money  have  you  altogether? 

Solve: 

13.  |+i  =  ?  17.  f  +  i=?  21.  |-i=?  25.  4xi=? 

14.  i  +  f=?  18.  f-|  =  ?  22.  i-i=?  26.  3XJ  =  ? 

15.  Ki=?  19.  l-i  =  ?  23.  |-|  =  ?  27.  6Xi=? 

16.  i  +  |  =  ?  20.  |-i=?  24.  |-i=?  28.  3Xf=? 


ADDITION  AND  SUBTRACTION.  147 

REVIEW. 

182.  Add: 

1.  88,  492,  744,  799,  277,  558,  772,  534,  887,  87,  65. 

2.  599,  540,  489,  775,  957,  898,  388,  745,  764,  88,  88, 

3.  544  +  868  +  454  +  334  +  558  +  663  +  854  + 156  +  594  + 

288=? 

4.  878  +  925  +  848  +  89  +  295  +  975  +  424  +  989  +  529  +  98 
+  973=? 

Find  the  sum  of : 

5.  989,  587,  659,  884,  497, 958,  52,  598,  844,  68,  65. 

6.  799,  947,  864,  577,  959,  795,  495,  844,  577,  58,  4. 
.7.  559,  675,  576,  543,  76,  345,  975,  34,  486,  98,  965. 

MENTAL   EXERCISE. 

183.  Subtract: 

21     32    43    54    61     72     83     94     100 
>55555555        5 


21 

32 

43 

54 

65 

90 

100 

6 

6 

6 

6 

6 

6 

6 

21 

32 

43 

54 

65 

76 

100 

7 

7 

7 

7 

7 

7 

7 

Note..— Do  the  following"  work  in  class: 

Subtract :   91027300467193450014 
17263398720456901029 

230091402130680970013520 
128940080956198296746936 


148 


ADDITION  AND  SUBTRACTION. 


Subtract :   33310201010063452960013 
12100617289113856972869 


EXERCISE. 

1  84.  Find  the  difference : 

1.  4287003   2.  3010604 
3650169      1720456 


4.  8001641 
7100956 

7.  3596001 
2100998 


5.  9340106 
5340508 

8.  2684302 
1008697 


3.  4284006 
3639109 

6.  5017603 
979184 

9.  3001801 
2018697 


REVIEW. 

185.  Read  sums  rapidly : 
32    42    52    62    83    93    63    53    43    33    103 
869796875      98 


44    54    64    74    85    95    65    35    25    105 
_9_6_8J7_9^_8^_9_7 

Read  the  differences  in  the  above  rapidly. 

Add: 

5,  9,  9,  2,  9,  9,  8,  4,  9,  8,  2,  7,  3,  9,  7,  9. 

9,  9,  4,  9,  9,  5,  9,  7,  4,  8,  2,  9,  7,  7,  2,  2. 

7,  5,  8,  9,  5,  8,  9,  4,  9,  7,  4,  6,  4,  7,  0,  8. 

9,  5,  8,  9,  7,  5,  4,  5,  3,  9,  8,  4,  5,  3,  0,  7. 

3,  9,  4,  4,  6,  1,  4,  6,  4,  3,  5,  3,  9,  4,  4,  3,  2,  5,  3. 

4,  7,  6,  2,  3,  8,  9,  1,  5,  4,  1,  7,  4,  8,  2,  6,  4,  3,  5. 
9,  9,  2,  9,  2,  9,  7,  4,  5,  4,  6,  4,  5,  4,  1,  9,  3,  8. 


ADDITION  AND  SUBTRACTION.  149 

(1)         (2)         (3)         (4)         (5)        (6)         (V)         (8) 

854  697  576  797  799  436  478  975 

376  482  648  346  423  644  584  476 

785  748  542  553  853  751  558  729 

456  284  345  474  124  244  867  589 

755  459  856  426  489  865  984  593 
556  789  464  745  534  496  949  549 
752  429  984  585  928  724  579  685 
596  789  459  259  296  998  844  548 

756  687  695  389  988  713  859  895 
456  757  659  534  464  249  679  245 

9.  798  +  557  +  789  +  985  +  557  +  78  +  895  +  559  +  849  +  96 
+  85=? 
Add: 

10.  589, 457,  855,  587,  658,  545,  758, 89,  599, 99,  54. 

11.  58,  79,  594,  957,  85,  474,  545,  874,  689,  77,  8. 

12.  599,  759, 575,  557,  254,  788,  357,  785,  587,  78, 4. 

13.  557,  640,  555,  579, 459,  808,  879,  955, 909,  87, 4. 

14.  45,  575,  678,  554,  508,  370,  757,  545,  959,  86,  54. 

15.  987,  895,  956, 967, 485,  54,  875,  580, 97, 9,  3. 

EXERCISE. 

186.  1.  In  what  year  was  your  schoolhouse  built? 
How  many  years  have  passed  since  that  time? 

2.  How  many  years  have  passed  since  the  discovery  of 
America  b}^  Columbus  in  1492? 

3.  A  farmer  went  to  town  with  a  load  of  wood,  which  he 
sold  for  $8.  He  bought  25  pounds  of  sugar  for  $2,  eight 
pounds  of  raisins  for  $1,  two  pounds  of  tea  for  $1.50,  and 
six  pounds  of  coffee  for  $2.10;  how  much  did  he  spend? 
Did  he  receive  for  his  wood  enough  to  pay  for  his  groceries  ? 


150 


ADDITION  AND  SUBTRACTION. 


4.  A  grocer  bought  50  barrels  of  apples  and  100  boxes 
of  peaches,  for  which  he  paid  $225.  If  he  paid  $75  for  the 
peaches,  how  much  did  he  pay  for  the  apples? 

5.  Bought: 


4  lb.  butter,  @  22  c. 
21b.  cheese,  ''  18  c. 
3  doz.  eggs,  ''  15  c. 
9  qt.  milk,  "  6  c. 
2  bu.  potatoes,  '^  65  c. 
2  bu.  carrots,    ^'  60  c. 

What  was  the  amount  of  my  bill? 
6.  Bought: 


9  lb.  rice, 

2  "  tapioca, 

3  '^  sago, 
5  "  sugar, 
7  '^  prunes, 
3  "  figs. 


(3  7  c. 
''  15  c. 
''  13  c. 
''  9  c. 
''  9  c. 
''  15  c. 


What  was  the  amount  of  my  bill? 

7.  Bought: 

41b.  tea,  @  $1.25  . 

2  ''  coffee,      ''       .42  . 

2  '^  raisins,     '^       .11  . 

7  '^  currants,  '^       .09  . 

5  '^  crackers,  ^^       .12  . 

7  "  sugar,       ^^       .08  . 

What  was  the  whole  amount? 


ADDITION  AND  SUBTRACTION.  151 

8.  Fill  in  the  total: 

]3cMA>^  c4 13.  5.  dttoTV  ^  Gcv., 


I   .54- 

.c]0 

M-.80 

.80 
\.25 


2  u>UXcMA>  tpoub^kd^,  @  Li-5^ 

I  n/Ji/rY\/YYi<><yk>    .      . 

I    tcX^OTV  TVUMAKAy 

1  \/jJ(tV 

I  a-jaxuie/ 

13.  S.  OXte/n.  ^  (V. 

9.  Complete  the  bill: 

Nashville,  Tenii.,  Feb.  10, 1904. 
Mr.  John  Mitchell, 

Bought  of  J.  D.  Hunt  &  Co., 

2  lb.  coffee,        @  32  c $ 

6  ^^  crackers,    ^Ml  c 

3  ''  honey,        ^M8  c 

1  ^^  Japan  tea .98 

1  doz.  oranges .40 

1  sack  flour        3.89 

Received  payment, 

J.  D.  HUNT  &  CO. 


152  MULTIPLICATION  AND  DIVISION, 

MULTIPLICATION  AND  DIVISION. 

EXERCISE. 

187.  1.  Multiply  478  by  624. 

478  X  4  units    =     1912  units 
478  478  X  2  tens     =      956    tens 

524  478  X  6  hund.  =  2868     hundreds 

Jg J2  478  X  624         =  298272  units 

QKA  The  second  partial  product  =  9560  units.     The 

oogg  third  partial  product  =  286800   units.      It  is  not 

necessary  to  write  the  zeros,  since  the  place  in 

298272        which  each  figure  is  written  gives  its  value ;  6  in 
tens'  place  is  the  same  as  60  units. 

2.  Multiply  the  following  numbers  by  624: 

396, 489, 279,  486,  295, 197, 176,  294,  395, 284, 692, 986. 

3.  Multiply  by  798: 

276,  347, 468,987,  692,  985,  569,  696, 459,  879. 

4.  Multiply  by  718: 

698, 437, 329, 492, 682, 694, 987, 962,  764, 829,  677,  276. 

5.  Multiply  by  691 : 

218, 912, 986, 497,  319, 489, 637, 956,  739, 895, 989,  759. 

6.  Multiply  by  976: 

1241,  3124,  2312,  1342,  2137,  7125,  1259,  2138,  3216, 
4132, 5123,  3495, 4287,  5196. 

EXERCISE. 

188.  Divide  by  43: 

1.  34228    4.  29001    7.  302720     10.  261895 

2.  29439   5.  34675   8.  389580    11.  174604 

3.  21389    6.  347010   9.  34718    12.  302290 


MULTIPLICATION  AND  DIVISION. 


153 


Divide  by  53: 

13.  51756   16.  44877  19.  50880 

14.  34363    17.  32305  20.  41376 

15.  25349    18.  33920  21.  480180 

Divide  by  54:         ' 

25.  21457    28.  41565  31.  43445 

26.  37729    29.  37719  32.  32934 

27.  41541    30.  48978  33.  41564 


22.  42888 

23.  39723 

24.  36994 


34.  21456 

35.  37728 

36.  32933 


EXERCISE. 

189.  Divide  by  35: 

1.  16231    4.  26581    7.  31737    10.  32848 

2.  22664    5.  34510    8.  31176    11.  24455 

3.  32847    6.  24456   9.  16800    12.  26582 

Divide  by  45: 

13.  35839   16.  41024   19.  43650    22.  28379 

14.  31032   17.  31708   20.  38700    23.  36288 

15.  43847   18.  36289   21.  22077    24.  43651 

Divide  these  numbers  by  55  and  65. 


EXERCISE. 

190.  1.  What  is  the  value  of  8950  bushels  of  wheat,  at 
95  cents  per  bushel? 

2.  A  commission  house  sold  75  bushels  of  cranberries, 
at  $2.75  cents  per  bushel;  how  much  money  was  received? 

3.  $4320  was  paid  to  54  men  for  one  month's  work  in 
building  a  bridge;  how  much  money  did  each  man  receive? 


154      ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

4.  B  paid  $25668  for  land,  at  $46  an  acre;  how  many 
acres  did  he  buy? 

5.  What  is  the  value  of  870  barrels  of  apples,  at  $3.75 
per  barrel? 

6.  A  wholesale  house  sold  1260  pairs  of  blankets  in  one 
month,  at  $4.50  a  pair;  how  much  money  was  received 
from  these  sales? 

7.  There  are  1272  pupils  in  a  school  building  and  53 
pupils  in  each  room;  how  many  rooms  are  there  in  the 
building? 

8.  The  distance  from  A  to  B  is  936  miles.  If  I  travel  at 
the  rate  of  36  miles  an  hour,  in  how  many  hours  can  I  com- 
plete the  journey? 

9.  When  oranges  are  selling  at  $3.50  a  box,  what  must 
be  paid  for  598  boxes? 

10.  $1479  was  spent  for  rugs,  at  an  average  cost  of  $17 
each;  how  many  rugs  were  purchased? 


ADDITION  AND  SUBTRACTION  BY  ENDINGS 

191.  6  +  9, 

Add: 

5     15    25    35    45    55    65     75    85    95 
9999999999 


Make  a  subtraction  table,  taking  9  from  each   of  the 
results  of  the  above  addition. 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.      155 
Add: 


(1) 

(2) 

(3) 

(4) 

(5) 

797 

958 

87 

768 

355 

950 

885 

855 

55 

478 

545 

878 

87 

557 

587 

457 

559 

995 

495 

55 

575 

949 

4 

954 

967 

84 

750 

775 

569 

98 

895 

565 

957 

45 

755 

55 

947 

79 

479 

889 

497 

787 

598 

89 

898 

67 

655 

85 

82 

62 

Add: 

6.  895, 258, 978, 45,  554, 645, 546, 795, 606, 8, 4. 

7.  958, 545, 758,  789, 478, 959,  570, 295, 906, 59, 4. 

8.  989, 959, 575, 487, 55, 597,  897, 905, 897, 687, 75. 

9.  895, 587, 798, 855, 566, 855, 975, 989, 589, 95. 

10.  989, 455, 464, 955, 587, 768, 555, 789, 587, 898, 75. 

11.  989, 597, 855, 867, 558, 485, 986, 505,  798, 597, 74. 


(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

325 

515 

585 

995 

959 

899 

598 

959 

515 

587 

575 

575 

512 

151 

954 

798 

689 

856 

955 

555 

151 

455 

552 

789 

195 

599 

959 

787 

784 

585 

915 

911 

191 

378 

499 

897 

255 

155 

515 

595 

585 

594 

457 

535 

995 

556 

348 

854 

575 

287 

277 

688 

787 

89 

977 

242 

347 

565 

465 

65 

156        ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

REVIEW. 
192.  Read  sums  rapidly: 

32    42    52    62    83    93    63    53    43    33     103 

44    54    64    74    85    95    65    35    25    105 

Read   differences  rapidly. 

Add: 

5,  9,  9,  2,  9,  9,  8,  4,  9,  8,  2,  7,  3,  9,  7,  9. 

9,  9,  4,  9,  9,  5,  9,  7,  4,  8,  2,  9,  7,  7,  2,  2. 

7,  5,  8,  9,  5,  8,  9,  4,  9,  7,  4,  6,  4,  7,  0,  8. 

9,  5,  8,  9,  7,  5,  4,  5,  3,  9,  8,  4,  5,  3,  0,  7. 

3,  9,  4,  4,  6,  1,  4,  6,  4,  3,  5,  3,  9,  4,  4,  3,  2,  5,  3. 

4,  7,  6,  2,  3,  8,  9,  1,  5,  4,  1,  7,  4,  8,  2,  6,  4,  3,  5. 
9,  9,  2,  9,  2,  9,  7,  4,  5,  4,  6,  4,  5,  4,  1,  9,  3,  8. 

(1)    (2)    (3)    (4)    (5)    (6)    (7)    (8) 

854  697  576  797  799  436  478  957 

376  482  648  346  423  644  584  476 

785  748  542  553  853  751  558  729 

456  284  345  474  124  244  867  589 

755  459  856  426  489  865  984  593 
556  789  464  745  534  496  949  549 
752  429  984  585  928  724  579  685 
596  789  459  259  296  998  844  548 

756  687  695  389  988  713  859  895 
456  757  459  534  464  249  679  245 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.      157 

9.  798  +  557  -f  789  +  985  +  557  +  78  +  895  +  559  +  849  +  96 
+  85=? 

Add: 

10.  589, 457,  855,  587,  658,  545,  758,  89,  599, 99,  54. 

11.  58,  79,  594,  957,  85,  474,  545, 874,  689,  77,  8. 

12.  599,  759,  575,  557,  254,  788,  357,  785,  587,  78, 4. 

13.  557,  640,  555,  579,  459,  808,  879,  955,  909,  87, 4. 

14.  45,  575,  678,  554,  508,  370,  757,  545,  959,  86,  54. 

15.  987,  895, 956, 967, 485,  54,  875,  580, 97, 9,  3. 

REVIEW. 

193.  Add,  beginning  at  the  left: 

9,    9,  4,  9,  9,  4,  7,  8,  4,  8,  3,  7,  3,  8,  6,   4. 

7,    7,  9,  9,  8,  4,  8,  8,  3,  7,  3,  8,  7,  4,  6,    1. 

4,    6,  7,  3,  9,  4,  9,  2,  8,  2,  7,  9,  4,  8,  8,    7. 

4,   9,  9,  3,  4,  4,  6,  4,  8,  3,  7,  3,  8,  9,  9,    2. 

6,    6,  6,  4,  8,  9,  4,  6,  4,  8,  7,  4,  5,  4,  7,    3. 

4,    8,  9,  9,  8,  4,  6,  3,  6,  4,  3,  7,  3,  8,  2,    6. 

6,    7,  6,  2,  4,  8,  3,  9,  4,  4,  9,  4,  8,  9,  3,    5. 
Add: 

(1)         (2)         (3)         (4)         (5)         (6)         (V)         (8)         (9) 

483  495  497  794  298  646  594  384  799 

628  418  782  288  418  443  764  384  423 

982  499  839  839  499  574  435  348  853 

148  744  242  274  744  437  474  314  124 

482  394  879  997  394  649  544  958  489 

644  424  449  434  424  767  347  328  534 

966  494  894  939  494  424  854  733  928 

188  428  324  977  428  396  334  493  298 

447  787  998  799  787  787  788  889  988 

357  653  338  764  653  567  568  269  462 


158  ADDITION  AND  SUBTRACTION. 

(10)  (11)  (12)  (13)  (14)  (15)  (16)  (17)  (18)  (19) 

436  989  798  873  889  999  934  498  496  787 

644  322  979  845  944  844  844  844  844  444 

751  877  292  149  233  455  955  467  984  485 

244  713  933  952  724  488  488  327  985  575 

865  442  244  347  243  319  544  943  438  824 

496  983  759  732  863  942  223  168  578  493 

724  524  282  444  143  243  935  484  314  899 

998  554  444  244  933  354  194  343  993  422 

713  627  489  536  259  386  938  348  119  644 

249  978  879  878  778  979  968  798  688  549 


REVIEW. 

194.  Read  sums  rapidly: 

21  32  43  54  65  76  87  100 

888   8   888    8 


21     32     43     54     65     76     87     98     100 
99999999        9 


Read  differences  rapidly. 

Subtract :    132964021347625010026 
92467395689706110958 


86213507010013426598312 
63152710236647258698595 

Note. — Do  this  in  Class. 


ADDITION  AND  SUBTRACTION. 


159 


195.  Subtract: 

1.  5010026 
2110958 

4.  2937111 
1930086 

7.  6010028 
4110869 

10.  3674021 
1690084 

13.  8100118 
1909099 


EXERCISE. 

2.  3004210 
1910096 

5.  6101034 
3908956 


3.  9721011 
8120699 


8.  7010039 
6110699 

11.  2901003 
1889019 


14.  7010165 
3927896 

EXERCISE. 


6. 

4010024 
3110859 

9. 

8621011 
7620388 

12. 

1807007 
918069 

15. 

5900011 
2574698 

196.  1.  Three  men  buy  some  land  for  $75000;  the  first 
pays  $25000,  and  the  second  pays  $17500;  how  much  does 
the  third  man  pay? 

2.  How  much  must  I  add  to  $12690  to  enable  me  to  buy 
a  farm  valued  at  $15000? 

3.  A  has  $125,  B  has  $79  more  than  A,  and  C  has  as  much 
as  A  and  B;  how  much  money  have  A,  B,  and  C  together? 

4.  A  train  travels  758  miles  a  day  for  the  first  three  days 
of  the  week,  and  695  miles  a  day  for  the  remaining  four 
days;  how  far  has  the  train  traveled  in  a  week? 

5.  I  paid  $6800  for  a  lot  and  built  a  house  which  cost 
$9500;  the  street  improvements  cost  me  $500.  For  how 
much  must  I  sell  the  house  and  lot  in  order  to  gain  $2000? 


160  MULTIPLICATION  AND  DIVISION. 

6.  Add  49170,  33040,  45215,  and  8315;  and  take  the  sum 
from  265780. 

7.  The  sum  of  two  numbers  is  185674;  one  of  the  num- 
bers is  92750;  what  is  the  other  number? 

8.  The  difference  between  two  numbers  is  18698;  one  of 
the  numbers  is  9740;  what  is  the  other  number? 

9.  The  remainder  is  6793;  the  subtrahend  is  6755;  what 
is   the   minuend? 

10.  The  minuend  is  7848;  the  remainder  is  6702;  what 
is  the  subtrahend? 

MULTIPLICATION  AND  DIVISION. 
19*7.  Copy  and  complete  the  following  tables: 


3X13= 

3X14  = 

3X15  = 

3X16 

4X13  = 

4X14  = 

4X15  = 

4X16 

5X13= 

5X14  = 

5X15  = 

5X16 

6X13= 

6X14  = 

6X15= 

6X16 

7X13  = 

7X14= 

7X15= 

7X16 

8X13= 

8X14  = 

8X15= 

8X16 

9X13= 

9X14  = 

9X15= 

9X16 

3X17 

3X18 

3X19 

= 

4X17 

4X18 

4X19 

= 

5X17 

5X18 

5X19 

= 

6X17 

6X18 

6X19 

= 

7X17 

7X18 

7X19 

= 

8X17 

8X18 

8X19 

= 

9X17 

9X18 

9X19 

= 

These  tables  may  be  used  as  an  aid  in  finding  any  term  of  the 
quotient. 


MULTIPLICATION  AND  DIVISION. 


161 


EXERCISE. 

198.  1.  Divide  by  13:  3844,  1456,  2899,  3241,  4869, 
12980. 

2.  Divide  by  14:  4899,  1386,  3287,  1642,  1196,  10896. 

3.  Divide  by  15:  3453,  1296,  1484,  4192,  1483,  14080. 

4.  Divide  by  16:  4686,  2825,  4242,  4339,  1509,  12243. 

5.  Divide  by  17:  4198,  2649,  9497,  1562,  1678,  14909. 

6.  Divide  by  18:  3584,  3291,  6183,  7139,  1796,  89010. 

7.  Divide  by  19:  3764,  3698,  7501,  1368,  1509,  94055. 


EXERCISE. 

199.  Divide  by  26: 

1.  12447    4.   8046    7.  19492 

2.  24336    5.  25239    8.  24338 

3.  19491    6.  12443    9.  25230 


Divide  by  36: 

10.  24461    13.  28251  16.  38440  19.  28252 

11.  32331    14.  26666  17.  33497  20.  38441 

12.  35507    15.  14689  18.  32330  21.  33495 


Divide  by  46: 

22.  22421    25.  34353  28.  32422  31.  44620 

23.  34481    26.  41216  29.  41704  32.  39100 

24.  18325    27.  28033  30.  36369  33.  28034 


162 


MULTIPLICATION  AND  DIVISION. 


EXERCISE. 


200.  8094X208=? 


8094 
208 


208  =200  +  8 
8094  X      8  =      64752 
8094  X  200  =  1618800 


64752 
16188 

1683552  (product). 


Find  products: 

1.  2965X204 

2.  3472X409 

3.  5409X508 

4.  5696X607 

5.  2897X906 

6.  3587X609 

201. 


8094  X  208  =  1683552  product. 
It  is  not  necessary  to  write  the  zeros  in 
the  second  ])artial  product.    We  write  the 
8  in   hundreds'   place.      8  in  hundreds' 
place  has  the  same  value  as  800  units. 


7.  3098X709 

8.  4037X694 

9.  6089X358 

10.  2064X708 

11.  2022X109 

12.  4967X907 

EXERCISE. 


13.  3048X308 

14.  6497X309 

15.  3859X276 

16.  9294X709 

17.  6789X608 

18.  3008X907 


To  multiply  by  10,  100,  1000,  etc. ,  annex  as  many  zeros  to  the 
multiplicand  as  there  are  zeros  in  the  multiplier. 

Find  products : 

1.  345X10      4.  783X300    7.  249X1000     10.  369X4000 

2.  386X100    5.  846X500    8.  728X2000     11.  484X7000 

3.  985X100    6.  782X900    9.  689X5000    12.  299X6000 


202. 


EXERCISE. 


To  divide  by  10,  100,  1000,  etc.,  cut  off  from  the  right  of  the 
dividend  as  many  figures  as  there  are  ciphers  in  the  divisor.  The 
part  cut  olf  is  the  remainder  ;  the  rest  of  the  dividend  is  the 
quotient. 


MULTIPLICATION  AND  DIVISION. 


163 


Divide  each  of  the  following  numbers  by  10,  100,  and 
1000: 


1.  24865 

2.  35642 

3.  21870 

4.  64823 


5.  46704 

6.  39405 

7.  38400 

8.  96099 


9.  10398 

10.  26405 

11.  30240 

12.  43442 


13.  65143 

14.  84291 

15.  75028 

16.  63000 


EXERCISE. 


203.  Divide  by  27: 


1.   9845    4. 

23751 

1  . 

21349 

10. 

207700 

2.  12844    5. 

20770 

8. 

22680 

11. 

237511 

3.  17478    6. 

281430 

9. 

218430 

12. 

984500 

Divide  by  37: 

13.  17205    16. 

32426 

19. 

29940 

22. 

18130 

14.  23514    17. 

31442 

20. 

32930 

23. 

335604 

15.  24959    18. 

35817 

21. 

299349 

24. 

335609 

Divide  by  47 : 

25.  17129    28. 

41332 

31. 

32308 

34. 

413320 

26.  36438    29. 

28530 

32. 

40847 

35. 

285300 

27.  37520    30. 

32845 

33. 

41830 

36. 

375250 

EXERCISE. 

204.  Divide  by  57: 

1.  48306     4.  28229     7.  483066    10.  282290 

2.  39540     5.  51098     8.  395400    11.  510980 

3.  48279     6.  55794     9.  482799    12.  557944 


164         HALVES,  THIRDS,  FOURTHS,  AND  SIXTHS. 


Divide  by  67: 
13.    23765  18.    32126 


14.  43102 

15.  31040 

16.  31901 

17.  57945 


19.  56768 

20.  42814 

21.  56731 

22.  65554 


23.  58266 

24.  60157 

25.  63543 

26.  46793 

27.  32868 


EXERCISE. 


205.  Divide  by  68: 
1.  29631     6.  31805 


2.  23517 

3.  43343 

4.  36331 

5.  50084 


7.  44015 

8.  51978 

9.  56955 
10.  50900 


11.  59489 

12.  46754 

13.  66504 

14.  61059 

15.  64367 


28.  408059 

29.  540690 

30.  467688 

31.  635219 

32.  648560 


16.  65317 

17.  46240 

18.  59179 

19.  65307 

20.  59177 


COMPARISON  OF  HALVES,   THIRDS,  FOURTHS,  AND 
SIXTHS. 

206.  Into  how  many  equal  parts  is 
this  circle  divided? 

One  of  the  twelve  equal  parts  of  any 
thing  is  called  what?  One  half  of  the 
circle  is  how  many  of  these  parts? 

One  third  of  the  circle  is  how  many 
twelfths  of  the  whole  circle. 

i  is  how  many  twelfths? 

I  is  how  many  twelfths? 

Which  is  more,  J  of  a  cake  or  J?    ^  or  i? 

207.  Look  at  the  circle  and  find   the  answers  to  these 
questions : 

Note. — This  may  also  be  studied  with  a  circle  cut  from  paper 
and  folded  into  halves,  then  into  sixths,  then  into  twelfths. 


HALVES,  THIRDS,  FOURTHS,  AND  SIXTHS.  165 


1.  ^  and  i  are  how  many  twelfths? 

2.  ^  and  j  are  how  many  twelfths? 


3.  i+i=?  6.  f  +  i  =  ?  9.  t  +  A=?  12.  i|-A=? 
4.1+1=?  7.  i  +  J=?  10.  f  +  A=?  13.  1-A  =  ? 
5.  i+iV=?     8.  |  +  i  =  ?     11.  f-A=?      14.     1-  |=? 

15.  Alice  cut  out  ^  of  a  cake  to  take  to  a  picnic;  her 
mother  used  J  of  the  cake  for  tea.  What  part  of  the  whole 
cake  was  left? 

16.  Edgar  used  ^  of  a  ball  of  twine,  and  his  brother  Carl 
used  J  of  the  ball;  what  part  of  the  whole  ball  was  left? 

208.  Look  at  the  circle,  or  draw  a  circle,  and  find 
answers : 

1.  A  =  how  many  sixths?        4.  A  =  how  many  fourths? 

2.  A  =  how  many  fourths?      5.  ^t  =  how  many  sixths? 

3.  tV  =  how  many  halves?        6.  Find  J  of  ^  of  the  circle. 

7.  I  of  i  is  what  part  of  the  whole? 

8.  i  of  ^  is  what  part  of  the  whole? 

9.  iofi=?  10.  iofA=?  11.  4ofi=? 

12.  j%  is  found  in  j%  how  many  times? 

13.  tV  is  found  in  VV  how  many  times? 

14.  ii  contains  -i\  how  many  times? 

15.  1%^  contains  t%  how  many  times? 

16.  2  times  |  are  how  many  wholes? 

17.  4  times  f  are  how  many  wholes? 

18.  3XtV  are  how  many  twelfths?    How  many  wholes? 

19.  4Xf  are  how  many  wholes? 

20.  4X|=? 

21.  Which  of  these  forms  is  most  used:  If  or  §?  iV 
or  I? 


166  MISCELLANEOUS  PROBLEMS. 

MISCELLANEOUS    PROBLEMS. 

209.  1.  Four  boys  worked  together,  and  received  $3  for 
a  day^s  work.  If  they  divide  the  money  equally,  what  part 
will  each  receive?    How  many  cents  will  each  receive? 

2.  $9  is  i  of  my  money ;  how  much  money  have  I? 

3.  5  qt.  is  J  of  all  the  berries  James  has  to  sell;  how 
many  quarts  has  he? 

4.  George  and  his  two  cousins  received  a  present  of  2 
watermelons;  they  divided  them  equally;  what  was  the 
share  of  each?     (Make  a  drawing.) 

5.  May,  John,  and  Ella  gathered  2  pecks  of  nuts  and 
divided  them  equally;  what  was  each  one's  share? 

6.  George  says,  ^^61  marbles  is  14  more  than  all  I  have.'' 
How  many  marbles  has  he? 

7.  A  boy  standing  30  feet  from  the  edge  of  the  water,  shot 
an  arrow  to  an  island  40  feet  from  the  shore.  How  far 
must  he  go  in  walking  and  rowing  to  get  the  arrow? 

8.  How  far  must  he  go  to  get  the  arrow  and  return  to  the 
place  of  starting? 

9.  Bought  10  yd.  of  silk  for  $9.50,  and  lOJ  yd.  of  cloth 
for  $5.25;  how  much  more  did  the  silk  cost  than  the 
cloth? 

10.  A  man  owing  $1000  made  2  payments,  one  of  $180 
and  one  of  $260;  how  much  remained  unpaid? 

11.  A  planing-mill  sells  680  ft.  of  pine  lumber,  845  ft.  of 
poplar,  398  ft.  of  cherry,  480  ft.  of  ash,  560  ft.  of  walnut, 
746  ft.  of  maple.     How  many  feet  are  sold? 

12.  A  farmer  sold  26  dozen  eggs  at  22^  cents  a  dozen, 
and  16  pounds  of  butter  at  28^  cents  a  pound.  How  much 
did  he  receive  for  them? 


DIVISION 


167 


DIVISION. 


EXERCISE. 


210.  Divide  by  49: 


1.  17353 

2.  22725 

3.  22922 


4.  31093 

5.  43280 

6.  31297 


7.  42972 

8.  47479 

9.  37247 


10.  43610 

11.  398410 

12.  333200 


Divide  by  59: 

13.  38072 

14.  27582 

15.  46393 


16.  40030 

17.  41162 

18.  46393 


19.  40041 

20.  41182 

21.  29311 


22.  509170 

23.  377600 

24.  .476189 


EXERCISE. 


311.  Divide  by  69: 


1.  24442 

2.  30053 

3.  36894 

4.  32085 


6.  32104 

7.  46506 

8.  25991 

9.  47442 


11.  59871 

12.  58443 

13.  66723 

14.  51718 


5.  25142   10.  53015   15.  59999 


16.  61871 

17.  65469 

18.  558210 

19.  54547 

20.  654690 


EXERCISE. 


212.  Divide  by  74: 


1.  25597 

2.  32227 

3.  54503 


4.  34330 

5.  34596 

6.  63955 


7.  58201 

8.  71669 

9.  70125 


10.  255970 

11.  345966 

12.  701250 


168  ADDITION  AND  SUBTRACTION  BY  KNDINOS. 


Divide  by  78: 

13.  36140 

14.  28439 

15.  57079 

16.  35595 

17.  52641 


18.  36480 

19.  58841 

20.  53625 

21.  58413 

22.  75458 


23.  60040 

24.  53769 

25.  68598 

26.  54500 

27.  73991 


28.  67820 

29.  30622 

30.  685980 

31.  754580 

32.  355951 


ADDITION  AND  SUBTRACTION  BY  ENDINGS. 
313.  6  +  6. 


Add: 


6    16    26    36    46    56    66    76    86    96 
6-666666666 


Make  a  subtraction  table,  taking  6  from  each  of  the 
results  obtained  above. 

Add: 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

96 

965 

955 

7659 

6989 

4665 

594 

224 

436 

4444 

5659 

7654 

662 

655 

596 

7363 

8346 

4469 

259 

386 

695 

6735 

3653 

7653 

569 

596 

39 

.  6646 

673 

4986 

756 

765 

566 

8686 

968 

7866 

684 

939 

64 

7895 

6366 

6459 

566 

646 

995 

5563 

9681 

2794 

437 

356 

668 

8349 

7988 

9778 

79 

788 

999 

6879 

7687 

6899 

ADDITION  AND  SUBTRACTION  BY   ENDINGS.       169 

314.  6  +  7. 

Add: 

6     16    26    36    46     56     66     76    86    96 

Make  a  subtraction  table,  taking  7  from  each  of  the 
r(^sults  obtained  above. 


Add: 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

996 

967 

768 

997 

896 

6886 

767 

953 

437 

746 

9565 

4553 

577 

667 

762 

654 

433 

5665 

877. 

336 

255 

979 

7766 

636 

676 

57 

646 

469 

6568 

8387 

554 

656 

656 

463 

9895 

656 

983 

364 

765 

539 

4647 

9439 

767 

65 

276 

697 

676 

7475 

127 

889 

797 

678 

7568 

8518 

899 

79 

959 

988 

989 

798 

Add: 

7.  979, 969,  787,  696, 969,  878,  997,  788,  979, 89. 

8.  76, 967, 899,  798,  697,  876, 968,  79,  577, 87, 9. 

9.  78, 969, 697,  786,  978,  869, 979,  779,  6,  89. 
10.  707, 966,  979, 799, 689,  76,  867,  978,  706, 66. 

215.  6  +  8. 

Read  endings;  then  sums: 

26    46    36    96    56    76    66    86     106 


170      ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

Make  a  subtraction  table,  taking  8  from  each  of   the 
results  of  the  preceding  addition. 

Add: 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

969 

688 

98 

666 

67 

58 

667 

363 

887 

664 

932 

9986 

536 

666 

686 

686 

6666 

4965 

594 

563 

439 

357 

6256 

7667 

468 

678 

967 

949 

4949 

6364 

666 

774 

936 

967 

6677 

5635 

546 

668 

866 

842 

6773 

6764 

788 

286 

546 

556 

6758 

7825 

98 

789 

797 

959 

6998 

899 

8 

869 

789 

688 

7957 

9 

Add: 

7.  89, 966,  878,  696,  788,  966,  787, 989, 89, 95. 

8.  899,  889, 869,  688, 986,  788,  769, 969, 88, 86. 

9.  689,  869,  788;  966, 687, 869, 978,  798,  789, 989. 
10.  899, 998, 866, 689, 969,  789,  669, 898, 678, 668. 

216.  6+9. 

Add: 

6     16    26    36    46    56    66     76    86    96 
_9_9^_9999999 

Make  a  subtraction  table,  taking  9  from  each  of  the 
results  obtained  above. 


MISCELLANEOUS  PROBLEMS.  171 


Id: 
(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

889 

67 

799 

896 

6 

6 

896 

936 

981 

9695 

65 

963 

986 

194 

616 

5338 

636 

9616 

696 

619 

996 

664 

7464 

7366 

868 

766 

268 

6937 

39 

6987 

769 

759 

399 

9996 

6699 

7586 

996 

996 

663 

6668 

8965 

9936 

897 

399 

567 

977 

8898 

7999 

97 

717 

868 

7196 

8766 

9965 

6 

89 

978 

878 

988 

899 

MISCELLANEOUS  PROBLEMS. 

217.  1.  -\  of  21  + J  of  40  are  how  many? 

2.  Bought  6  bars  of  soap  for  a  quarter  of  a  dollar;  what 
will  12  bars  cost  at  the  same  rate? 

12  bars  are  2  times  6  bars ;  then,  12  bars  cost  2  times  25  cents, 
or  50  cents. 

3.  James  had  72  cents.  He  spent  ^  of  it  for  a  new  book, 
and  ^  for  pencils;  what  part  did  he  spend?  How  many 
cents  has  he  left? 

4.  A  colt  was  bought  for  $60,  and  sold  for  IJ  times  its 
cost;  what  was  the  gain? 

5.  What  will  f  of  35  pears  cost,  at  3  cents  each? 

6.  What  will  f  of  a  gallon  of  vinegar  cost,  at  9  cents  a 
quart? 

7.  A  market  woman  bought  4  quarts  of  berries  for  40 
cents,  and  sold  them  at  6  cents  a  pint;  how  much  did  she 
gain? 


172 


DIVISION. 


8.  How  many  minutes  are  there  in  tV  (or  j)  of  an  hour? 

9.  3i  dozen  are  how  many  times  7?  At  the  rate  of  7 
marbles  for  9  cents,  what  will  3J  dozen  cost? 

10.  I  have  66  cents.  If  I  spend  A  of  it  for  a  pound  of 
butter,  how  much  will  I  have  left? 

11.  If  12  cents  is  \  of  the  cost  of  a  book,  what  will  6 
books  cost? 

12.  At  7i  cents  an  ounce,  what  will  4  ounces  of  nutmegs 
cost? 

13.  A  grocer  buys  8  barrels  of  apples,  7  times  as  many 
barrels  of  potatoes,  and  i  as  many  barrels  of  turnips  as 
potatoes.     How  many  barrels  of  turnips  does  he  buy? 

14.  Frank  had  $2.80.  He  spent  i  of  it  for  a  cap,  \  of  it 
for  a  ball,  and  with  the  remainder  bought  a  book;  how 
much  did  the  book  cost? 

DIVISION. 

EXERCISE. 

218.  Divide  by  79: 

1.  27985        6.   28814  11.  59160  16.  74734 

2.  34394        7.   42392  12.  66881  17.  54469 

3.  36081        8.    53274  13.  56441  18.  75651 

4.  50993        9.    51130  14.  66976  19.  60818 

5.  44619       10.    54292  15.  66191  20.  77922 


EXERCISE. 

219.  Divide  by  84: 

1.  38971        4.   47676  7.  71069  10.  79548 

2.  29192        5.   62693  8.  64597  11.  476760 

3.  54881        6.    57557  9.  81315  12.  813150 


DIVISION. 


173 


Divide  by  87: 

13.  39691   16.  56338  19.  56423  22.  42369 

14.  36193   17.  58716  20.  82465  23.  587160 

15.  66603   18.  59582  21.  69145  24.  845800 


230o  Divide  by  89: 

1.  30718 

2.  38784 

3.  57300 

4.  47574 

5.  32415 


EXERCISE. 

6.  56507 

7.  50244 

8.  57481 

9.  58280 
10.  56574 


11.  59965 

12.  66431 

13.  60034 

14.  68072 

15.  42443 


16.  67303 

17.  60380 

18.  78040 

19.  60418 

20.  77212 


21.  57749 

22.  65729 

23.  86137 

24.  86910 

25.  61379 


Divide  by  97: 

26.  44987  29.  46240  32.  66723  35.  67784 

27.  61565  30.  73397  33.  84186  36.  87096 

28.  62838  31.  76290  34.  77296  37.  841860 


221. 


EXERCISE. 


1.  Divide  by  200:  36472,22365,96284,87986,76384. 

2.  Divide  by  300:  39672,44281,67243,88752,67971. 

3.  Divide  by  120:  36448,29676,32439,28795,78134. 

4.  Divide  by  130:  72941,63214,72811,93214,81719. 

5.  Divide  by  125 :  76255,  83245, 96312, 84354,  26989. 

6.  Divide  the  numbers  in  problem  5  by  135;  by  150. 


174  UNITED  STATES  MONEY. 

UNITED  STATES  MONEY. 

222,  What  is  the  cost  of  a  bushel  of  apples,  if  5  bushels 
are  sold  for  $6? 

This  means  finding  one  of  the  five  equal  parts  of  $6,  or  600  cents. 

5 )  $6.00,  cost  of  five  bushels. 

$1.20,  cost  of  one  bushel. 

If  the  dividend  contains  no  cents,  annex  two  ciphers,  separated 
from  dollars  by  a  period.  Divide  as  in  simple  numbers,  and 
separate  dollars  from  cents  in  the  quotient. 

1.  *  of  $416.35=?    4.  i  of  $219.18=?     7.  |  of  $625.17=? 

2.  1  of  $312.24=?    5.  i  of  $916.25=?     8.  i  of  $909.20=? 

3.  J  of  $700.17=?    6.  i  of  $813.24=?     9.  i  of  $805.10=? 

223.  1.  When  sugar  is  selling  at  5  cents  a  pound,  how 
many  pounds  can  be  bought  for  $6? 

This  means  finding  the  number  of  times  5  cents  ($.05)  are  found 
in  600  cents,  or  $6. 

$.05  )  $6.00 

120 
120  pounds  of  sugar  at  5  cents  a  pound  can  be  bought  for  $6. 

2.  At  $1.30  a  pair,  how  many  pairs  of  gloves  can  be 

bought  for  $6? 

$1.30)  $6.00  (4 
5.20 
80  cents  remaining. 
4  pairs  of  gloves  can  be  bought,  with  80  cents  remaining. 

3.  At  $1.30  cents  a  yard,  how  many  yards  of  cloth  can 
be  bought  for  $6.00? 


UNITED  STATES  MONEY,  175 

$1.30)16.00(4 
5.20 
80  cents  remaining. 

Four  yards  of  cloth  can  bo  bought  for  $6.00,  with  80  cents 
remaining. 

If  we  make  a  complete  division  and  spend  all  the  money,  we 
have : 

$1.30)6.00(4A 
6.00 

80 
4  yards  and  A  of  one  yard  can  be  bought  for  $6. 

EXERCISE. 

224.  1.  If  6  boxes  of  oranges  are  sold  for  $21,  what  is 
the  value  of  one  box? 

2.  I  bought  20  yards  of  carpet,  for  which  I  paid  $9.80; 
what  was  the  price  of  one  yard? 

3.  At  49  cents  a  yard,  how  many  yards  of  flannel  can  be 
bought  for  $10.50? 

4.  When  wheat  is  selling  at  87  cents  a  bushel,  how  many 
bushels  can  be  bought  for  $1200? 

5.  At  $1.50  a  barrel,  how  many  barrels  of  potatoes  can 
be  bought  for  $60? 

6.  At  $1.87  a  yard,  what  will  325  yards  of  carpet  cost? 

7.  $391.50  was  paid  for  87  bushels  of  clover  seed;  what 
was  the  cost  per  bushel? 

8.  If  the  clover  seed  was  sold  at  $5  per  bushel,  what  was 
the  gain  on  87  bushels? 

9.  Watermelons  are  selling  at  wholesale  for  $8  per  hun- 
dred; what  is  the  value  of  one  melon? 

10.  If  these  melons  are  sold  at  retail  at  15  cents  each, 
what  is  the  gain  on  180  melons? 


176 


SQUARE  MEASURE. 


SQUARE  MEASURE. 

One  square  yard. 


'I'i'i'i'i'i 
ii'i'i'i'i'i 

225,  Mark  on  the  schoolroom  floor,  or  on  the  black- 
board, a  square  which  shall  measure  a  yard  on  each  side. 
This  is  called  a  square  yard. 

Divide  the  square  yard  into  9  equal  squares,  as  shown 
in  the  above  figure.  Each  one  of  these  squares  measures 
how  much  on  each  side? 

Each  one  of  these  squares  is  called  a  square  foot. 

A  square  yard  is  how  many  square  feet? 

9  sq.  ft.  =  1  sq.  yd. 


SQUARE  MEASURE.  177 

226.  1.  1  square  foot  is  what  part  of  1  square  yard? 

2.  If  you  should  set  out  9  geraniums  in  a  garden  bed  a 
yard  square,  how  much  ground  could  you  allow  for  each 
plant,  allowing  the  same  amount  for  each?  (Make  a  draw- 
ing.) 

3.  How  many  square  feet  are  there  in  2  square  yards? 

4.  How  many  square  feet  in  3  square  yards? 

5.  Draw  on  the  board,  or  on  the  floor  of  the  schoolroom, 
3  square  feet;  inclose  a  space  3  feet  square.  Which  is  the 
larger  space?    How  many  times  as  large? 

6.  Draw  and  compare  2  square  feet  with  a  space  2  feet 
square. 

227.  Cut  out  of  paper  a  square  which  is  1  foot  on  each 
side.     How  many  inches  is  it  on  each  side? 

Cut  a  square  which  is  one  inch  on  each  side.      This  is 
1  inch.  called  a  square  inch. 

Fold  your  square  foot  of  paper 
into  square  inches. 

First,  into  how  many  1-inch  strips 
shall  you  fold  it? 

One   square   foot   is   how   many 
square   inches? 


1  square  inch. 


This  figure  is  a  square  incli  iu  size. 

1  sq.  ft.  =  144  sq.  in. 

228.  1.  Inclose  a  space  on  the  board,  which  shall  be 
1  foot  square.  Divide  this  square  foot  into  square  inches. 
How  many  square  inches  are  there? 

2.  Find  out  how  many  small  squares  of  patchwork,  each 
four  inches  square,  can  be  cut  from  a  square  foot  of 
calico. 


178  MISCELLANEOUS  PROBLEMS. 

3.  How  many  of  these  squares  can  be  cut  from  a  square 
yard  of  calico? 

4.  My  slate  is  9  inches  long  and  7  inches  wide ;  how  many 
square  inches  of  surface  has  it?  There  are  7  rows  of  9 
square  inches.     7  times  9  square  inches  =  63  square  inches. 

5.  Find  the  area  (surface)  of  a  flower  bed  which  is  6  feet 
long  and  2  feet  wide. 

6.  The  length  of  a  flower  bed  is  5  feet;  the  area  15  square 
feet.     What  is  the  width?     (Make  a  drawing.) 


MISCELLANEOUS    PROBLEMS. 

229.  1.  How  many  pounds  of  sugar  at  6  cents  a  pound 
can  be  bought  for  9  yards  of  calico  at  12  cents  a  yard? 

2.  How  many  pairs  of  shoes  at  $3.00  a  pair  must  be  given 
in  exchange  for  30  bushels  of  potatoes  at  50  cents  a 
bushel  ? 

3.  A  farmer  sold  to  a  grocer  19  bushels  of  apples  at  75 
cents  a  bushel,  and  took  his  pay  in  coffee  at  30  cents  a 
pound.     How  many  pounds  did  he  receive? 

4.  A  milkman  sells  daily  50  quarts  of  milk  at  4  cents  a 
quart.  How  many  yards  of  carpet  at  $1.00  a  yard  can  be 
bought  for  the  milk  sold  in  a  month  of  30  days? 

5.  For  12-days'  work  a  workman  received  $24.  At  that 
rate,  how  much  would  he  receive  for  18-days^  work? 

6.  Mr.  Jones  sold  121  pounds  of  beef  at  14  cents  a  pound, 
and  took  his  pay  in  potatoes  at  77  cents  a  bushel;  how 
many  bushels  did  he  receive? 

7.  A  grocer  sold  150  pounds  of  sugar,  at  8  cents  a  pound. 
How  many  pounds  of  tea  must  he  sell,  at  60  cents  a  pound, 
to  equal  the  amount  he  received  for  the  sugar? 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.       179 

8.  How  much  can  I  save  in  a  year,  if  I  earn  $140  each 
month  for  ten  months,  and  spend  $68.63  each  month  for  12 
months? 

9.  What  will  2  bushels  of  berries  cost,  at  12^  cents  a 
quart? 

10.  A  man  bought  28  boxes  of  lemons  at  $5.25  per 
box,  and  sold  them  at  $4.68  per  box;  how  much  did  he 
lose? 

11.  12  X  12  X  12  =  ? 

12.  If  I  save  5  cents  a  day,  how  much  shall  I  save  in  19 
years? 

13.  A  commission  house  spends  $30  a  day  for  telegrams; 
how  much  is  spent  in  65  days? 

14.  If  12  men  earn  $72  in  one  week,  how  much  will  18 
men  earn  in  the  same  time? 

15.  How  many  square  feet  of  surface 
has  the  floor  of  the  room  represented  by 
this  drawing? 

16.  How  many  square  yards  of  oil- 
cloth will  be  required  to  cover  the  floor? 

Addition  and  subtraction  by  endings. 

230.  7  +  7. 

Read  endings;  then  sums: 

7    27    37    47    57    67    77    87    97    107 


Make  a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  7  from  each. 


180      ADDITION   AND  SUBTRACTION  BY   ENDINGS. 


1: 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

777 

795 

779 

996 

998 

766 

377 

548 

637 

576 

8979 

8735 

747 

877 

765 

455 

6613 

7269 

496 

743 

659 

979 

6267 

7637 

673 

676 

575 

192 

5772 

572 

357 

834 

924 

626 

6386 

9826 

787 

797 

777 

473 

7676 

7466 

774 

272 

565 

856 

8476 

887 

637 

956 

776 

69 

997 

7988 

789 

879 

986 

9 

859 

978 

231.  7  +  8. 

Read  endings;  then  sums: 

.     7    27    37    47    57    67    77    87    97     107 

888888888        8 


Make  a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  8  from  each. 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

888 

888 

778 

669 

789 

6789 

777 

382 

223 

179 

6846 

6677 

443 

627 

879 

768 

7973 

9826 

978 

365 

458 

795 

4769 

3667 

726 

967 

764 

987 

6268 

9547 

789 

194 

228 

876 

8666 

6978 

621 

797 

977 

754 

9568 

8779 

775 

777 

842 

478 

7599 

978 

647 

949 

498 

729 

975 

74 

689 

589 

798 

978 

89 

9 

MISCELLANEOUS  PROBLEMS, 


181 


232.  7  +  9. 

Read  endings;  then  sums: 

7    17    27    37    47    57    67    77    87    97     107 


9 


9      9      9 


9 


Make   a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  9  from  each. 


Add: 
(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(•7) 

999 

977 

988 

789 

794 

9779 

97 

776 

296 

979 

189 

9685 

9979 

686 

245 

872 

777 

756 

8546 

6877 

399 

777 

187 

448 

257 

8767 

6777 

769 

833 

956 

776 

764 

6794 

864 

267 

999 

797 

129 

657 

9467 

6468 

988 

632 

427 

794 

775 

1895 

9736 

233 

769 

984 

669 

867 

8736 

798 

777 

647 

227 

778 

978 

6759 

9797 

97 

989 

898 

976 

598 

988 

986 

89 

MISCELLANEOUS    PROBLEMS. 

233.  1.  Bought: 


25  lb.  of  sugar, 

@  7c. 

11    ''    tea, 

''   48c. 

12    ''     coffee, 

''    23c. 

22    '^  raisins. 

''    He. 

19    ''  currants. 

"   9c. 

18    ^'  crackers. 

''    12c, 

What  is  the  amount  of  my  bill? 

182 


MISCELLANEOUS  PROBLEMS. 


2.  Bought: 

12  lb.     of  dried  apples, 
14  doz.   "  eggs, 
32  qt.      "  milk, 
9  bu.     "  potatoes, 
12  lb.      ''  butter, 
11  lb.      ^^  cheese, 

What  is  the  amount  of  my  bill? 


3.  Bought: 

9  bbl.  of  apples, 

12  bu.  ^'  plums, 

9    ^'  "  peaches, 

20    ''  ''  cherries, 

12    ''  ''  pears, 

11     '^  ^^  quinces. 
What  was  the  whole  amount? 


@ 


@  9c. 
"    15c. 
"    6c. 
"    65c. 
"    22c. 
''    18c. 


$2.15 
1.20 
1.75 
1.05 
1.35 
1.50 


4.  Complete  the  bill: 

Cincinnati,  O.,  Aug.  27,  1903. 
Mr.  John  Norris, 

Bought  of  Charles  E.  Scott  &  Co., 
3  student  lamps,                   @  $3.75      ...      .      .    $ 
1  doz.  knives  and  forks,         "      4.25 
1  doz.  plated  teaspoons,        '^     2.65      .... 
1  refrigerator, 12.75 

1  lawn  mower, 6.10 

2  rakes,  $0.68  and  $0.93, 

1  step-ladder, 1.75 


Received  payment, 

CHARLES  E.  SCOTT  &  CO. 

per  John  M.  Austin. 


MISCELLANEOUS  PROBLEMS.  183 

5.  Complete  the  bill: 

Cincinnati,  O.,  Oct.  31,  1903. 
Mr.  James  C.  Martin, 

Bought  of  Lloyd,  Watson  &  Co., 
9  yards  of  cassimere,  @  $2.85 

12  yards  of  pressed  flannel,    ^^        .58      .      . 
11  yards  of  black  silk,  ^'      1.65 

2  pairs  of  hose,  ''        .75,  $1.25 

1  cloak, 

1  pair  of  blankets, 

6  handkerchiefs,  ^'        .50      .      . 

9  linen  towels,  '^        .35 


18.00 
6.75 


Received  payment, 

LLOYD,  WATSON  &  CO. 
w. 

6.  A  lady  bought  2  yards  of  ribbon  at  37  cents  a  yard, 
6  yards  of  muslin  at  19  cents  a  yard,  3  yards  of  flannel  at 
35  cents  a  yard,  5  yards  of  lace  at  98  cents  a  yard,  some 
needles  for  31  cents,  and  a  belt  for  75  cents;  what  did  her 
purchases  amount  to?    Make  out  the  bill. 

7.  Bought  a  pair  of  boots  for  $8.50,  an  umbrella  for  $3.62, 
a  pair  of  gloves  for  $1.25,  some  collars  for  $0.75,  and  a  hat 
for  $4;  what  did  all  cost?     Make  out  the  bill. 

8.  Bought  8  yards  of  velvet  at  $1.25,  4  yards  of  satin  at 
$1.85,  6  yards  of  Spanish  lace  at  $0.87,  and  7  yards  of  sateen 
at  $0.38.     Make  out  the  bill. 

9.  Mr.  John  R.  Holt  bought  of  Hains  &  Co.,  6  dozen 
oranges  at  28  cents  a  dozen,  4  pounds  of  tea  at  75  cents  a 
pound,  8  lamp  chimneys  at  10  cents  each,  10  pounds  of 
crackers  at  9  cents  a  pound,  5  pounds  of  coffee  at  35  cents 


184      ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

a  pound,  and  8  pounds  of  starch  at  20  cents  a  pound.     Make 
out  the  bill. 

10.  The  value  of  my  farm  is  J  the  value  of  my  house  and 
lot.  If  the  farm  is  worth  $3600,  what  is  the  value  of  the 
house  and  lot? 

11.  If  the  remainder  is  17,  the  quotient  75,  and  the  divi- 
dend 45767,  what  is  the  divisor? 

12.  A  man,  having  $18432,  deposited  in  bank  $558,  and 
with  the  remainder  bought  land  at  $54  an  acre  ;  how 
many  acres  did  he  buy? 

234.  8  +  8. 

Read  endings;  then  sums: 

8    18    28    38    48    58    68    78    88    98 

Make  a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  8  from  each. 

Add: 

(1)         (2)         (3)         (4)         (6)         (6)  (7) 

787  698  988  878  878  97  77 

439  797  675  636  889  7719  9998 

978  685  799  987  386  8778  8794 

828  878  479  957  879  8653  7347 

584  154  988  969  787  4877  5865 

748  488  843  768  687  7777  7179 

886  728  788  856  995  4859  2759 

686  871  788  949  297  8796  9578 

738  348  919  786  798  89  628 

988  899  899  877  768  7  HS 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.      185 

235.  8+9. 

Read  endings;  then  sums: 

8     18    28    38    48    58    68    78     88    98 
_?_^_?_^_^J     1    ^    ^    ^ 

Make  a  subtraction  table  by  using  the  results  of  the 
above  addition  and  subtracting  9  from  each. 

1.  Add  899,  283,  998,  158,  895,  887,  728,  993,  947,  989. 

2.  Find  the  sum  of  78,  8887,  9988,  9763,  8989,  8989, 
8799,  95,  9887,  48,  988. 

3.  Add  767,  6512,  9899,  8269,  768,  6938,  9799,  8967,  937, 
8788. 

4.  Find  the  amount  of  89,  6478,  9878,  7468,  9826,  9676, 
9832,  7989,  899,  7. 

5.  679  4-  695  +  977  +  889  +  649  +  877  +  778  -f  898  +  879  + 
879=? 


Add: 


(6)  (7)  (8)  (9)  (10)  (11)  (12) 

899  8  9  78   767  89  679 

283  839  979  8887  6512  6478  695 

998  SS8  83  9988  9899  9878  977 

158  889  848  9763  8269  7468  889 

895  393  889  8989   768  9826  649 

887  868  738  8799  6938  9676  877 

728  474  996  95  9799  9832  778 

993  987  897  9887  8967  7989  898 

947  859  58  48  937  899  879 

989  79  69  988  8788  7  879 


386 


SUBTRACTION. 


MENTAL     EXERCISE. 

236.  Subtract: 

21    32    43    54    65    76    100    81    95    64 
676678        8987 

91    84    42    67    96    87    45    83    100 
87698967        9 

243510098290003881 
184376591462388887 

304009623076592800069 
126993611159677863599 

Note. — Do  this  in  class. 


Find  remainders : 

1.  62101011 
52781096 


2.  66330490 
29001695 


3.  32505607 
23809108 


4.  35210101     5.  75004132    6.  8849060 
2671908       6217779        157386 


7.  97800110 
1901906 


8.  87096247 
3504768 


9.  93808706 
76709809 


10.  62001091 
41901698 


11.  32100901 
12901967 


12.  30103055 
22768996 


CUBIC  MEASURE. 


187 


CUBIC  MEASURE. 

237.  How  many  faces  has  a  cube?  What  is  the  form 
of  each  face? 

How  many  edges  has  a  cube? 

How  many  corners  has  a  cube? 

Find  a  cube  whose  edges  are 
each  one  inch  long. 

A  cube  whose  edges  are  each 
one  inch  long  is  called  a  cubic 
inch. 


238.  1.  Build  a  post  of  one-inch  cubes;  how  high  a 
post  will  3  such  cubes  make? 

2.  One  cubic  inch  is  what  part  of  the  post?  2  cubic 
inches  ai^  what  part  of  the  post? 

3.  Make  a  post  of  one-inch  cubes;  how  high  a  post  will 
4  such  cubes  make? 

4.  One  cubic  inch  is  what  part  of  the  post?  2  cubic 
inches  are  what  part  of  the  post? 

5.  How  many  cubic  inches  are  there  in  2  posts,  if  each 
contains  4  cubic  inches? 

6.  How  many  one-inch  cubes  are  there  in  a  block  3 
inches  long,  3  inches  wide,  and  3  inches  high?  (Build  with 
inch   cubes.)      How   many    1-inch 

cubes  in  J  of  the  block? 

7.  How  many  cubic  inches  in  a 
block  of  wood  4  inches  long,  1  inch 
wide,  and  1  inch  thick? 

8.  How  many  cubic  inches  in  a 
block  4  inches  long,  2  inches  wide. 


,y  y  y 


hm^ 


188  MISCELLANEOUS  PROBLEMS. 


and  1  inch  thick?    How  many  rows      ^^^^ ^^ y 
of  4  cubic  inches  each? 

9.  How  many  cubic  inches  in  a 
block  4  inches  long,  2  inches  wide, 
and  2  inches  thick? 


2  times  4  cubic  inches  =    8  cubic  inches. 
2  times  8  cubic  inches  =  16  cubic  inches. 

10.  Build  a  solid  4  inches  long,  4  inches  wide,  and  4  inches 
high;  how  many  cubic  inches  will  it  contain?  Measure  the 
distance  round  it. 

11.  How  many  1-inch  cubic  blocks  can  you  pack  in  a 
box  which  is  4  inches  long,  4  inches  wide,  and  4  inches  high? 

12.  How  many  1-inch  cubes  of  candy  can  you  place  in  a 
box  6  inches  long,  4  inches  wide,  and  4  inches  high,  measur- 
ing on  the  inside  of  the  box? 

13.  Build  a  solid  of  one-inch  cubes  which  shall  be  12 
inches  long,  12  inches  wide,  and  1  inch  high;  how  many 
cubes  are  used? 

MISCELLANEOUS    PROBLEMS. 

239.  1.  If  40  men  can  do  a  piece  of  work  in  10  days,  in 
what  time  could  8  men  do  the  same  work? 

2.  My  farm  contains  120  acres;  yV  of  it  is  in  meadow, 
W  in  wheat,  and  the  rest  in  woodland.  What  part  is  wood- 
land?   How  many  acres  are  woodland? 

3.  A  stationer  bought  12  dozen  pens  at  5  cents  a  dozen, 
and  sold  them  at  two  for  a  cent;  what  did  he  gain? 

4.  I  had  $120.  I  spent  \  of  it  for  a  watch,  \  of  it  for  an 
overcoat,  and  i%  of  it  for  board;  how  much  had  I  left? 


MISCELLANEOUS  PROBLEMS,  189 

5.  A  man  had  a  dozen  boxes  of  candy,  each  box  con- 
taining 10  pounds.  If  he  makes  of  it  packages  containing 
one-half  pound  each,  how  many  packages  will  he  have? 

6.  A  man  carried  4|  pecks  of  cherries  to  market,  and  sold 
them  at  ten  cents  a  quart;  how  much  did  he  receive  for 
them? 

7.  At  2  cents  a  square  foot,  what  will  8  square  yards  of 
wire  cloth  cost? 

8.  Find  the  cost  of  10  yards  of  calico  at  14  cents  a  yard, 
and  8  yards  of  ribbon  at  20  cents  a  yard. 

9.  A  lady  paid  J  of  a  dollar  for  a  thimble,  |  of  a  dollar  for 
braid,  and  -^^  of  a  dollar  for  thread ;  how  much  money  did 
she  spend? 

10.  James  had  $100,  and  spent  \  of  it  for  a  watch  and 
ipo  for  a  coat;  how  much  money  did  he  have  left? 

11.  If  11  cents  is  ^  of  the  cost  of  a  basket,  what  will  5 
baskets  cost? 

12.  If  6  apples  cost  5  cents,  how  many  apples  can  I  get 

for  50  cents? 

50  cents  is  10  times  5  cents ;  10  times  6  apples,  or  60  apples,  can 
be  bought  for  50  cents. 

13.  What  will  be  the  cost  of  natural  gas  for  8  months  on 
one  cook-stove  at  $1  a  month,  two  grates  at  $1.25  each  per 
month,  and  one  base-burner  at  90  cents  per  month? 

14.  If  a  boy  earns  $12  a  month,  how  much  will  he  earn 
in  a  year?  If  he  spends  i  of  his  earnings  for  clothes  and 
board,  how  much  will  he  have  left? 

15.  Bought  10  bushels  of  peaches  at  $1  a  bushel,  and  sold 
them  at  30  cents  a  peck;  how  much  was  gained? 

16.  How  many  quarts  of  berries,  at  12  cents  a  quart,  will 
it  take  to  pay  for  8  yards  of  cloth,  at  16 J  cents  a  yard? 


190 


MULTIPLICATION  AND  DIVISION. 


MULTIPLICATION  AND  DIVISION. 

EXERCISE. 

340.  Find  quotients: 
1.     133215 -h107     11.    444280-^232     21.    766080^315 


2.    347655^-215 

12.    519013^319 

22. 

660303^423 

3.    809437^-621 

13.    923257^862 

23. 

735289+599 

4.    217892  H-493 

14.    707861-^639 

24. 

603972  -^224 

5.  1130493^533 

15.    753533^671 

25. 

487228-^827 

6.    653219-^394 

16.    219763-^995 

26. 

701101 +901 

7.    676175^215 

17.  3518599^  59 

27. 

684938^   98 

8.  1603008-^198 

18.  4519760-^196 

28. 

6503188+798 

9.  1529012^-189 

19.  5291234  H- 189 

29. 

1319229+189 

10.  4805019^789 

20.  8008191 -f- 129 

EXERCISE. 

30. 

6536479+129 

241.  Find  products: 

1.  12486X907 

6.    70009X907 

11. 

.  67201X1000 

2.  63579X786 

7.  280963X746 

12, 

,  26487X3002 

3.  39889X642 

8.  247560X985 

13. 

,  39865X1008 

4.  98270X876 

9.  476394X457 

14. 

,  90834X9020 

5.  62498X805 

10.  480976X805 

15. 

19598X8009 

ADDITION  AND  SUBTRACTION  BY  ENDINGS. 

242.  9+9. 

Read  endings;  then  sums: 

9  19  29  39  49  59  69  79  89  99 

Make  a  subtraction  table  by  using  the    results  of  the 
above  addition  and  subtracting  9  from  each. 


ADDITION  AND  SUBTRACTION  BY  ENDINGS.      191 


Add: 

1.  9998, 6799, 8798, 9789, 8989, 9987, 8899, 7899,  7027, 698. 

2.  7978,  5887,  7646, 9687, 9596, 6988, 8799, 7996,  7968, 967. 

24tS,   Subtract  and  read  endings: 

11     43    28    32    54    65    79    87    96     109 
999999999        9 


Subtract : 

1. 

88764- 

■  2969 

6. 

40031-  9594  11. 

10002- 

2999 

2. 

49875- 

■  2789 

7. 

58431-  3989  12. 

68003- 

9095 

3. 

37953- 

-  1896 

8. 

19052-  9298  13. 

90087- 

5069 

4. 

90585- 

13989 

9. 

90745-11989  14. 

19864- 

10989 

5. 

60103- 

-  389 

10. 

70001-  9867  15. 

90003- 

7648 

344.  Add: 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

28 

88 

38 

56 

29 

28292 

13977 

44189 

92 

32 

89 

69 

99 

94919 

88945 

99899 

19 

99 

93 

95 

92 

98189 

98288 

65288 

81 

88 

38 

56 

29 

28922 

33947 

76879 

28 

33 

89 

69 

99 

94889 

89885 

88968 

92 

89 

93 

95 

92 

98328 

99689 

47399 

19 

98 

38 

56 

29 

28994 

33641 

89863 

81 

33 

89 

69 

99 

94418 

98888 

66258 

28 

89 

93 

95 

92 

98999 

88697 

98898 

92 

91 

38 

56 

29 

28884 

33635 

75364 

19 

38 

89 

69 

99 

94937 

89889 

84959 

81 

99 

93 

95 

92 

98488 

99398 

66895 

28 

83 

38 

56 

29 

28992 

33533 

78386 

92 

39 

88 

69 

99 

94838 

88489 

95939 

19 

83 

95 

94 

95 

89985 

98982 

58897 

192  MISCELLANEOUS  PROBLEMS, 

Subtract: 

9.   1000101-  345879    12.  90148003-  9876435 

10.  80118181-  698197    13.  67100011-  400968 

11.  864121133-36849762    14.  810890890-20987689 

MISCELLANEOUS  PROBLEMS. 

245.  1.  A  hardware  store  sold  wire  amounting  to 
$161.46.  How  many  pounds  were  sold,  if  wire  was  worth 
$.18  a  pound? 

2.  A  hotel-keeper  paid  $52.44  for  38  table-covers.  How 
much  was  paid  for  each  one? 

3.  Mr.  Irvin  spent  $17.92  for  burlap  to  cover  the  walls 
of  his  library.  How  many  yards  were  used,  if  burlap  cost 
$.29  a  yard? 

4.  Mr.  Adam  collected  $104.49  from  a  dry-goods  house 
for  several  bolts  of  sheeting  sold  to  it.  How  many  yards 
were  bought,  if  the  sheeting  was  sold  at  $.27  a  yard? 

5.  In  a  certain  city  there  are  23,283  school  children. 
How  many  teachers  must  be  employed  to  teach  them,  if 
each  room  averages  39  children? 

6.  The  Agricultural  Department  in  Washington  bought 
enough  flower  seed  to  fill  476,160  packages.  How  many 
pecks  of  seed  were  needed,  if  96  packages  were  filled  from 
each  peck? 

7.  Last  September  a  factory  received  $309.66  from  the 
sale  of  penholders  in  Chicago.  They  were  worth  $.78  a 
gross.  How  many  gross  were  sent  there?  (A  gross  is  12 
dozen.) 

8.  A  retail  store  paid  $192.78  for  3  bolts  of  cloth,  each 
containing  54  yards.     How  much  was  paid  for  one  yard? 


MISCELLANEOUS  PROBLEMS  193 

9.  The  city  assessed  my  property  $194.04  for  98  square 
yards  of  asphalt  on  our  street.  How  much  was  paid  for 
every  square  yard  of  asphalt? 

10.  A  man  paid  $18,144  for  a  farm  of  96  acres.  What 
was  the  price  of  each  acre? 

11.  A  contractor  paid  $67.15  for  one-inch  nails.  The 
nails  were  woHh  $.85  per  hundred  pounds.  How  many 
hundred  pounds  were  bought? 

12.  There  are  172  feet  of  fine  wire  to  a  pound.  A  rail- 
road company  used  66,392  feet  during  the  year.  How 
many  pounds  were  used? 

13.  The  Atlas  Engine  Works  spent  $1,724.80  on  5i-inch 
bolts,  at  $17.60  per  hundred.  How  many  hundred  bolts 
were  used? 

14.  The  distance  from  Indianapolis  to  Chicago  is  196 
miles.  Last  year  an  engineer  covered  30,576  miles  of 
ground  on  his  trips  to  and  from  Chicago.  How  often  did 
he  cover  the  distance? 

15.  At  $2.98  a  pair,  how  many  pairs  of  shoes  must  a 
dealer  sell  to  receive  $551.30? 

16.  If  a  young  man  earns  $36  a  month,  in  how  many 
months  would  he  earn  $5608? 

17.  If  43  bu.  of  corn  cost  $15.91,  what  does  1  bu. 
cost? 

18.  How  many  wagon  loads  of  corn  containing  41  bu. 
can  be  filled  from  a  bin  containing  1066  bu.? 

19.  It  is  1392  mi.  from  here  to  a  certain  place.  How 
long  will  it  take  to  get  there,  if  we  travel  at  the  rate  of 
48  mi.  an  hour? 

20.  If  41  men  do  a  piece  of  work  for  $69.29  a  day,  what 
does  one  of  these  men  earn? 


194  MISCELLANEOUS  PROBLEMS. 

21.  If  a  bin  of  wheat  is  worth  $5086.90,  how  many 
bushels  does  it  contain,  when  wheat  is  selUng  at  $.65  per 
bu.? 

22.  How  many  bushels  of  wheat  worth  $.64  are  in  a  bin 
valued  at  $469.92? 

23.  If  69  bu.  of  corn  cost  $50.96,  what  does  1  bu.  cost? 

24.  If  it  is  2990  mi.  from  here  to  San  Francisco,  how 
long  will  it  take  to  get  there,  traveling  at  the  rate  of  46 
mi.  an  hour? 

25.  A  man  had  $65060;  he  spent  $1905,  and  purchased 
land  at  $65  per  A.  with  the  remainder.  How  many  acres 
did  he  buy? 

26.  A  farmer  having  91  acres  of  land  sold  ^  of  it  for 
$30940.     What  did  he  receive  per  acre? 

27.  I  sell  I  of  my  farm  of  168  A.  for  $5796.  What  is 
the  price  per  A.? 

28.  A  man  sold  86  baskets  of  grapes  for  $30.10.  For 
how  much  did  he  sell  one  basket? 

29.  A  surface  contains  1431  sq.  yd.  and  is  27  yd.  wide; 
how  long  is  it? 

30.  How  wide  is  a  hall  that  contains  414  sq.  ft.  and  is 
23  ft.  long? 

31.  A  floor  13  ft.  wide  contains  871  sq.  ft.  How  long 
is  it? 

32.  A  surface  contains  1677  sq.  ft.  and  is  43  ft.  long. 
How  wide  is  it? 

33.  I  sold  84  barrels  of  potatoes  for  $134.40  and  lost 
$12.60.    What  was  the  cost  per  bbl.? 

34.  The  cost  of  raising  potatoes  was  $159.12.  If  they 
are  sold  in  36  bbl.  at  a  gain  of  $1.75  per  bbl.,  what  is  the 
selling  price  per  bbl.? 


ADDITION  AND  SUBTRACTION. 


195 


35.  The  cost  of  46  bu.  of  apples  is  $62.10.  They  are 
sold  at  a  gain  of  $.50  per  bu.     What  is  the  selling  price? 

36.  I  worked  18  weeks  at  $15.75  a  week,  and  saved 
$69.30  during  the  time.  How  much  did  I  save  per  week? 
What  were  my  weekly  expenses? 


DIVISION 

.  Find  quotients: 

1. 

774648  - 

-186 

9. 

614307- 

hl99 

2. 

295470- 

-190 

10. 

4722354  - 

^178 

3. 

937387  - 

-184 

11. 

2966607  - 

^189 

4. 

7210473  - 

-187 

12. 

713513- 

^179 

5. 

8043840- 

-194 

13. 

2154003  - 

^399 

6. 

842877  - 

-179 

14. 

1604083- 

=-987 

7. 

145260- 

-108 

15. 

685176- 

^197 

8. 

1874774- 

-172 

16. 

1260524- 

hl59 

17. 

17820- 

-294 

18.   632008  - 

:-196 

19.   657320  - 

-178 

20.   845679  - 

:-168 

21.  2474420  - 

=-307 

22.  15604064- 

Hl96 

23 

.   583700- 

=-395 

ADDITION  AND   SUBTRACTION. 

REVIEW. 

247.  1.  Add:  898,  983,  698,  867,  886,  259,  618,  886, 
989,  762  and  479. 

2.  Add:  464,  399,  987,  999,  878,  466,  598,  694,  726,  899, 

668  and  987. 


196  ADDITION  AND  SUBTRACTION. 

3.  695  +  944  +  899  +  978  +  627  +  489  +  398  +  772  +  786  + 
948  +  499  +  437  +  748  +  454=? 

4.  869  +  254  +  497  +  967  +  669  +  494  +  362  +  368  +  349  + 
688  +  547  +  174=? 


(5) 

(6) 

(7) 

(8) 

(e) 

278 

989 

868 

795 

768 

985 

747 

497 

867 

848 

374 

298 

682 

456 

494 

689 

884 

376 

967 

939 

567 

419 

488 

678 

826 

496 

568 

217 

893 

677 

439 

677 

168 

745 

988 

797 

486 

954 

878 

144 

765 

819 

849 

459 

899 

988 

948 

756 

868 

786 

642 

157 

867 

787 

278 

897 

764 

498 

214 

527 

(lO) 

(11) 

(12) 

(13) 

(14) 

526 

987 

278 

278 

2789 

788 

676 

148 

879 

6187 

144 

762 

126 

726 

9481 

889 

829 

475 

845 

8276 

496 

414 

987 

794 

5769 

968 

948 

276 

868 

8787 

684 

687 

279 

489 

9981 

845 

771 

476 

596 

6688 

496 

869 

278 

648 

1578 

989 

494 

219 

489 

4444 

878 

926 

798 

964 

9276 

727 

677 

694 

857 

8296 

MISCELLANEOUS  PROBLEMS.  197 


MISCELLANEOUS    PROBLEMS. 

248.  1.  If  a  man  earns  $8  a  week,  in  how  many  weeks 
will  he  earn  $96? 

2.  I  lost  $50  in  selHng  a  piano  for  $280;  what  was  the 
value  of  the  piano? 

3.  8  men  together  paid  $100  for  some  wheat;  if  they 
received  equal  shares  of  the  wheat,  what  should  each  man 
pay? 

4.  A  lady  bought  a  bushel  of  sweet  potatoes  for  $2.25, 
and  gave  in  payment  a  five-dollar  bill;  how  much  change 
should  she  receive? 

5.  Bought  20  yards  of  carpet  for  $40,  30  yards  of  cloth 
for  $75,  and  2  pairs  of  curtains  at  $16  a  pair;  what  did  I 
pay  for  all? 

6.  A  real-estate  agent  bought  some  land  for  $2000;  how 
much  will  he  gain,  if  he  divides  the  land  into  4  lots,  and 
sells  them  for  $600  each? 

7.  If  it  takes  one  man  100  days  to  do  a  piece  of  work,  in 
how  many  days  could  2  men  do  the  same  work,  working  at 

.  the  same  rate? 

8.  If  I  pay  6  cents  for  the  use  of  one  dollar,  what  should 
I  pay  for  the  use  of  5  dollars,  at  the  same  rate?  What  must 
I  pay  for  the  use  of  12  dollars? 

9.  I  borrowed  $100  for  a  year,  and  paid  6  cents  on  the 
dollar  for  its  use;  how  much  did  I  pay? 

10.  A  car  line  is  5  miles  long;  if  a  car  makes  12  round 
trips  daily,  how  many  miles  will  it  run  in  ten  days? 

11.  In  a  school  of  45  pupils,  |  are  present;  how  many  are 
absent? 


198  MISCELLANEOUS  PROBLEMS. 

12.  5  gallons  of  cream  were  sold  at  10  cents  a  pint; 
how  much  did  it  bring? 

13.  2  lemons  can  be  bought  for  5  cents;  at  that  rate, 
what  is  the  cost  of  2\  dozen? 

14.  At  30  cents  a  peck,  what  will  2J  bushels  of  apples 
cost? 

15.  My  lot  is  50  feet  wide,  and  four  times  as  long;  how 
many  yards  of  fence  will  enclose  it? 

16.  What  will  2  pounds  4  ounces  of  tea  cost  at  80  cents 
a  pound? 

17.  My  slate  has  a  surface  of  72  square  inches.  It  is 
12  inches  long;  how  wide  is  it? 

18.  I  have  a  box  6  inches  long,  4  inches  wide,  and  2  inches 
deep;  how  many  cubic-inch  blocks  will  it  hold? 

19.  A  sheet  of  paper  which  is  8  inches  wide,  has  a  surface 
of  96  square  inches;  find  the  length. 

20.  What  will  a  roast  of  6  pounds  of  beef  cost,  at  12 J 
cents  a  pound? 

21.  The  transom  above  the  door  is  3  feet  long  and  2  feet 
wide;  how  many  panes  of  glass  will  it  require,  if  each  pane 
is  1  foot  square?     (Drawing.) 

22.  How  many  cubic  inches  are  there  in  a  block  of  wood 
which  is  7  inches  long,  4  inches  wide,  and  2  inches  thick? 
(Drawing.)  If  the  block  were  3  inches  thick,  how  many 
cubic  inches  would  it  contain?  If  four  inches  thick,  how 
many  cubic  inches? 


REVIEW.  199 


249.  REVIEW. 

(1)  (2)  (3)  (4)  (5) 

271  274  4278  2789  2718 

487  169  8691  2219  476 

916  425  9547  6928  8679 

629  676  2648  9476  2764 

784  918  7927  4629  406 

848  215  9687  8742  579 

297  776  4948  7887  8719 

666  574  8976  6996  2778 

779  876  7476  9469  2789 

884  217  6216  1754  5476 

498  289  7364  4178  4769 

867  417  9785  2889  8769 


(6) 

("7) 

(8) 

(9) 

(lO) 

7248 

722 

125 

8627 

27694 

8961 

871 

672 

4578 

9678 

4476 

981 

897 

9694 

5761 

9941 

494 

778 

5278 

94876 

6698 

348 

444 

2419 

2765 

8269 

287 

998 

6265 

47698 

4884 

666 

626 

8555 

12789 

5446 

999 

269 

4278 

47687 

4998 

455 

855 

3987 

2767 

9824 

844 

114 

1876 

71001 

8767 

788 

748 

2947 

6843 

7287 

667 

856 

3782 

9874 

200 

DIVISION. 

Subtract: 

• 

11.  80005 

14.  103070   17.  90005 

20.  307561 

67421 

8524G       79008 

298728 

12.  100051 
87643 


13.  70005 
38729 


15.  60004 
38965 

16.  107302 

56927 


18.  207305 
189649 


19.  81012 
69299 


21.  78419 
69.593 


22.  415007 
387321 


DIVISION. 


250.  Find  quotients: 

1.  246573  H- 1212 

2.  745201  ^2373 

3.  1793257  ^6253 

4.  4175959  ^7329 

5.  9180257^6351 

6.  7221483  h-992 

7.  1250921 H-9253 

8.  27263579-^1371 


863973 

915761 

3621487 

8724165 

2153897 

14.  11853221 

15.  5995871 

16.  42507633 


9. 
10. 
11. 
12. 
13. 


^2652 
^2483 
^7193 
^3998 
^8253 
^8123 
^6751 
^8952 


17.  631253 

18.  2187923 

19.  4267942 
4250963 

793621 

22.  2170821 

23.  84371285 

24.  97239643 


20. 
21. 


^3251 
^2473 
^8198 
^9876 
^9957 
^6125 
^  695 
^9853 


MISCELLANEOUS  PROBLEMS.  201 

MISCELLANEOUS   PROBLEMS. 

251.  1.  How  many  years  is  it  from  the  time  of  the 
Centennial  exhibit  at  Philadelphia  in  1876  to  that  of  the 
Columbian  exhibit  at  Chicago  in  1893? 

2.  In  a  field  of  turnips  there  are  296  rows,  and  each  row 
yields  18  bushels;  how  many  loads  of  30  bushels  each  does 
the  field  yield? 

3.  $557283  added  to  a  certain  number  of  dollars  will 
produce  $1157003;  what  is  the  number? 

4.  If  68  pounds  of  coal  are  consumed  in  carrying  a  train 
one  mile,  how  many  pounds  will  be  consumed,  at  that  rate, 
in  going  1894  miles? 

5.  What  time  elapsed  from  the  battle  of  Lexington,  1775, 
to  the  firing  on  Fort  Sumter,  1861? 

6.  If  I  buy  real  estate  for  $854657,  agreeing  to  pay  for  it 
in  yearly  payments  of  $37159  each,  how  many  payments 
shall  I  make? 

7.  The  improved  land  of  the  United  States  is  estimated 
at  207198720  acres;  how  many  townships  of  23040  acres 
each  could  be  made  from  this  land? 

8.  In  a  pile  of  4701265  bricks,  how  many  loads  are 
there,  if  each  load  contains  1000  bricks? 

9.  145310 -1085=  ? 

10.  A  miller  purchased  2149  bushels  of  wheat,  weighing 
128940  pounds;  what  was  the  weight  of  1  bushel? 

11.  A  road  was  constructed  at  a  cost  of  $4328  per  mile, 
and  the  total  cost  was  $8331400;  how  many  miles  long  is 
the  road? 

12.  Find  the  sum  of  sixteen  million  one  thousand  twenty, 
twelve   million  one   hundred  twenty-eight,   nine   million 


202  MISCELLANEOUS  PROBLEMS. 

thirteen  thousand  two,  seven  milUon  sixteen  thousand 
seven,  and  three  hundred  million  nine. 

13.  The  President  of  the  United  States  receives  $50,000 
a  year;  how  much  is  that  a  day? 

14.  Fairview  Park  consists  of  480  acres,  for  which  $180,- 
000  was  paid;  how  much  was  that  per  acre? 

15.  If  46  acres  of  land  produce  2,484  bushels  of  corn,  how 
many  bushels  will  120  acres  produce? 

16.  There  are  30000  voters  in  a  city;  counting  this  as  one 
fourth  of  the  population,  what  is  the  population  of  the  city? 

17.  Lafayette  was  born  in  1757,  and  entered  the  Ameri- 
can army  in  1777;  how  old  was  he  at  that  time? 

18.  How  many  cubic  inches  are  there  in  a  block  of  ice 
2  feet  long,  2  feet  wide,  and  1  foot  thick? 

19.  The  population  of  Chicago  in  1890  was  1,099,850;  in 
1900  it  was  1,698,575.    Find  the  increase  for  ten  years. 


CHAPTER  VII. 

FRACTIONS. 

252,  What  name  is  given  to  numbers  which  represent 
parts  of  things,  as  J  of  a  dollar  or  |  of  a  field? 


By  means  of  these  figures,  review  the  relations  of 
halves,  fourths  and  eighths. 

How  many  halves  are  there  in  a  whole? 

How  many  fourths  in  a  whole  ?    In  a  half? 

How  many  eighths  in  a  whole  ?     In  a  half  ? 
In  a  fourth? 

Make  other  drawings  showing  halves,  thirds,  sixths  and 
twelfths,  and  compare  these  fractions. 

253.  % : — What  is  the  name  of  the  parts  in  this  fraction? 
(Eighths.) 

How  many  eighths  have  we?     (Six.) 

Write  the  number  in  such  a  way  as  to  show  that  it  is  a 
number  with  a  name.     (6  eighths.) 

$6;  6  books;  6  quarts: — Give  the  name,  or  the  denom- 
ination, of  each  of  these  quantities. 

What  is  the  denomination  of  6  eighths?  ,  (Eighths.) 


204  FRACTIONS. 

The  number  which  shows  the  name  or  the  denomination 
of  a  quantity  is  called  the  denominator. 

What  is  the  denominator  in  f?     (Eight.) 

Since  6  tells  the  number  of  things  that  we  have,  we  may 
call  it  the  ''numberer ''  or  the  numerator. 

What  is  the  numerator  in  f? 

Give  the  numerator  and  the  denominator  in  the  following: 

8  pencils;  5  dresses;  16  pints;  $7;   |;   f ;    r\;  4  hours; 

LIKE  AND   UNLIKE   NUMBERS. 

254.  Numbers  which  have  the  same  denominator  or 
name  are  like.  Numbers  which  have  different  denomina- 
tors or  names  are  unlike. 

Processes  Which  may  be  Performed  with  Like  Numbers. 

2^^.  $6  and  $2;  6  books  and  2  books;  6  quarts  and  2 
quarts;  6  eighths  and  2  eighths: — These  quantities  may  be 
added,  subtracted,  divided,  or  compared  by  subtraction  and 
division. 

1.  John's  coat  cost  $6  and  his  hat  $2.  How  much  did 
both  cost? 

2.  Mrs.  Jones  received  $6  for  her  weekly  expenses.  She 
had  $2  left.     How  much  did  she  expend? 

3.  At  $2  apiece,  how  many  books  can  be  bought  with  $6? 

4.  Harry  received  $6  for  a  Christmas  present.  Willie  re- 
ceived $2.  How  much  more  did  Harry  get  than  Wllhe? 
How  much  less  did  Willie  get  than  Harry? 

5.  I  paid  $6  for  a  hat  and  $2  for  a  pair  of  gloves.      The 


LIKE  AND   UNLIKE  NUMBERS,  205 

hat  cost  how  many  times  as  much  as  the  gloves?    The  cost 
of  the  gloves  is  what  part  of  the  cost  of  the  hat? 

Note. — Show  that  the  same  processes  may  be  performed  with 
fractions,  if  they  have  the  same  name  or  denominator.  Have 
the  pupils  make  problems  illustrating  all  of  the  fundamental 
processes,  first  with  integers  and  then  with  fractions. 

356.  Unlike  numbers  cannot  be  added,  subtracted,  di- 
vided or  compared. 

Can  these  processes  be  performed  with  6  pencils  and  2 
books? 

257.  Can  you  add  6  bushels  and  2  pecks?     (Yes.) 
What  must  be  done  before  these  quantities  can  be  added? 

(They  must  be  changed  to  the  same  measure.) 

6  bushels  =  24  pecks. 

24  pecks +  2  pecks  =  26  pecks. 

24  pecks— 2  pecks  =  22  pecks. 

24  pecks -^2  pecks=12. 

24  pecks  are  22  pecks  greater  than  2  pecks. 

2  pecks  are  22  pecks  less  than  24  pecks. 

24  pecks  are  12  times  2  pecks. 

2  pecks  are  V2  of  24  pecks. 

Can  these  processes  be  performed  with  ^  and  J?  Change 
the  fractions  to  the  same  measure,  say  fourths. 

Note. — Teachers  should  give  original  problems  showing  that 
fractions  not  having  the  same  name  may  be  changed  to  the  same 
name,  and  then  added,  subtracted,  divided,  or  compared. 

258.  Add,  subtract,  divide,  and  compare  the  follow- 
ing fractions  by  means  of  the  figures  on  p.  206,  pointing 
to  all  fractional  parts  named : 


206 


FRACTIONS, 


'/3 

% 


1    1 

H  1 

1    I 

j    1 

t  and  \ 
f  and  \ 
1  and  iV 
\  and  i^ 
\  and 
\  and 
J  and  \\ 
f  and  iV 
f  and  tV 
I  and  iV 


1  and  ^ 
1  and  \ 
\  and  \ 
\  and  f 
1  and  \ 
\  and  i 
\  and  f 
i  and  f 
\  and  I 
i  and  \ 

f  and  H 
\  and  iV 
i  and  ^^ 
\  and  1^ 
i  and  \\ 
I  and  1^ 


I  and 


tV 


I  and  tV 
f  and  H 
i  and  iV 


1 

1 

1 

1/, 

Vj 

1/2 

h 

^/c 

•ls\ 

5i 

1 

1 
1 

1 

• 

1 

1 

j 

^/J 

\  and  f 
\  and  f 
i  and  \ 
\  and  i 
\  and  f 
f  and  \ 
1  and  J 
1  and  \ 
\  and  i 
\  and  i 

i^  and  -^ 
\  and  tV 
i  and  \\ 
\  and  iV 
I  and  iV 
I  and  tV 
I  and  li 
4  and  \ 
\  and  f 
f  and  J 


REDUCTION, 


207 


REDUCTION. 


To  Change  Integers  and  Mixed  Numbers  to  Fractions. 

259.  1.  How  many  fourths  are  there  in  an  orange? 
How  many  fourths  in  6  oranges? 

2.  How  many  fifths  in  a  melon?     In  3  melons? 

In  one  melon  there  are  five  fifths ;  in  3  melons  there  are  three 
times  ^ve  fifths,  or  15  fifths. 

3.  How  many  sevenths  are  there  in  4?    In  6?    In  8? 

4.  How  many  eighths  of  an  apple  are  there  in  2f  apples? 


2|  apples  =  2  apples  and  |  of  an  apple.  In  one  apple  there  are 
eight  eighths.  In  two  apples  there  are  two  times  eight  eighths, 
which  are  sixteen  eighths.  Sixteen  eighths  and  three  eighths  are 
nineteen  eighths.     There  are  nineteen  eighths  in  2|  apples. 

Change : 

5.  3J  oranges  to  fifths  of  an  orange. 

6.  2f  apples  to  fourths  of  an  apple. 

7.  If  cakes  to  eighths  of  a  cake. 

8.  5g  feet  to  fifths  of  a  foot. 

9.  3f  yards  to  sevenths  of  a  yard. 

10.  3 1  gallons  to  ninths  of  a  gallon. 

11.  1^  gallons  to  fourths  of  a  gallon. 

12.  f  quarts  to  eighths  of  a  quart. 


208  FRACTIONS. 

260.  A  whole  number,  as  distinguished  from  a  fraction, 
is  called  an  Integer. 

A  Mixed  Number  is  an  integer  and  a  fraction  united;  as, 

An  Improper  Fraction  is  a  fraction  whose  numerator  is  as 
large  as,  or  larger  than,  its  denominator.  It  is  equal  to  one, 
or  more  than  one.    f,  |,  V,  and  ^  are  improper  fractions. 

261.  Change  to  improper  fractions: 

1.  2i        3i        51,        4f,        4i 

2.  6f,         5f,         7i,         31,         5i. 

3.  3f,        6t,        4f,         31,        5i 

4.  Change  to  eighths:  3,  2i,  3i,  4 J,  2f. 
5    Change  to  twelfths: 

3i,  2,  21,  4J,  5J, 

3A,         3f,  5,  25,  5i 

6.  Change  to  halves:  7,  4|,  2^  4|,  3 A- 

To  Change  Improper  Fractions  to  Integers  or  Mixed 
Numbers. 

262.  1.  How  many  pears  are  there  in  12  half-pears? 
In  13  half -pears? 

Tliere  are  two  half-pears  in  one  pear.  2  halves  are  in  13 
halves  6i  times.     Therefore,  there  are  6i  pears  in  13  half-pears. 

2.  How  many  gallons  are  there  in  6  half-gallons? 

3.  How  many  bushels  in  17  half-bushels? 

4.  How  many  melons  in  18  thirds  of  a  melon? 

5.  How  many  yards  in  17  thirds  of  a  yard? 

6.  How  many  ones  in  20  fifths?    In  28  fourths? 


REDUCTION.  209 

Change  to  integers  or  mixed  numbers: 

7.  i  V,  ¥,  ¥,  V. 

8.  V-,  ¥,  ¥,  ¥,  V. 

9.  ¥,  ¥,  V,  «,  ¥. 
10.  iJ.  f i  ¥,  ¥,  ¥. 

To  Change  Fractions  to  Higher  Terms. 

263.  To  reduce  to  higher  terms  is  to  change  a  fraction 
having  large-sized  parts  to  a  fraction  of  equal  value  having 
small-sized  parts. 

364.  1.  How  many  fourths  are  there  in  J  of  a  pie? 

There  are  4  fourths  in  one  pie.  In  i  of  a  pie  tliere  are  i  of  4 
fourths,  which  is  2  fourths,     i  of  a  pie  =  f  of  a  pie. 

Reduce : 

2.  J  to  eighths,  J  to  sixths,  |  to  twelfths. 

3.  ^  to  sixths,  f  to  sixths,  ^  to  ninths. 

4.  I  to  twelfths,  t  to  fifteenths,  f  to  eighteenths. 

5.  ^  and  J  to  sixths. 

6.  I  and  f  to  twelfths. 

265.  In  changing  to  higher  terms,  does  the  size  of  the 
parts  increase  or  decrease? 

Is  the  number  of  parts  increased  or  decreased? 

The  form  of  a  fraction  may  he  changed  without  changing  its 
value,  hy  multiplying  both  terms  hy  the  same  number.     Thus : 

1_1><4_4        2^2><3_6 
2     2X4~8        3~3X3~9 


210 


FRACTIONS. 


266.  1.  Reduce  J,  ^y  and  ^  to  equivalent  fractions  hav- 
ing the  same  sized  parts.  (What  is  the  meaning  of  the  word 
''equivalent'^?)  By  what  fractional  part  can  these  fractions 
all  be  measured? 

Determine  the  common  denominator  from  the  drawing. 


i-i. 

1 

1 
1 
1 
1 

1 

i 

i 

i  =  f. 

1 
1 

1 
1 

1 
1    1 

t^  =  tV 

Change  to  equivalent  fractions  having  a  common  measure 
or  denominator : 


2.  h  h  I 

3.  i,  I  h 

4.  I  h  f. 

5.  h  h  h 

6.  I  I  I 


7.  f,  tV,  iV- 

8.  A,  h  A. 

9.  i  i\,  i. 

10.  i,  \h  ^. 

11.  i  I  |. 


To  Change  Fractions  to  Lower  Terms. 

267.  To  reduce  to  lower  terms  is  to  change  a  fraction 
having  small-sized  parts  to  a  fraction  of  equal  value  hav- 
ing large-sized  parts. 

268.  1.  Two  quarters  of  a  dollar  are  the  same  in  value 
as  what  single  coin? 

2.  Two  quarters  of  an  apple,  when  placed  together,  are 
the  same  as  what  part  of  an  apple? 


REDUCTION, 
3.  Answer  the  following  from  the  drawings: 


211 


'k 

v^ 

\ 

^/^ 

Vs! 

'A\ 

!  i 

^       ?             i 

J 

9                   JL   _    ? 

f  =  ?          t  =  ?          A  =  ? 

V. 

1  =  ?        A  =  ?          A  =  ? 

1  =  ?         A  =  ?          if  =  ? 

!o 

In  the  answers  to  the  above  questions,  has  the  size  of  the 
parts  been  increased  or  decreased? 

Has  the  number  of  parts  been  increased  or  decreased? 

269.  Th£  form  of  a  fraction  may  he  changed  without 
changing  its  value j  by  dividing  both  terms  by  the  same  number. 
Thus: 

2232^1         ^_^±^_^ 
4"4-2     2        T5~15T3~5 

270.  1.  Reduce  1%  and  tV  to  fourths. 

2.  Reduce  2^1,  21,  and  J|  to  sevenths. 

3.  Reduce  if,  H,  if,  and  H  to  eighths. 

4.  Reduce  ^\,  A.,  if,  and  A  to  ninths. 

271.  When  a  fraction  is  reduced  to  an  equivalent  frac- 
tion with  smaller  terms,  it  is  reduced  to  lower  terms. 


212 


FRACTIONS. 


A  fraction  is  in  its  lowest  terms  when  no  number,  except  1, 
will  exactly  divide  both  its  numerator  and  its  denominator. 

Reduce  ^  to  lowest  terms. 

12h-2~6~6h-2~3  ^^  12^4    3 
f  is  the  fraction  in  its  lowest  terms. 

272.  Reduce  to  lowest  terms: 

1.  tV,  tV,  i,  A,  A 

2.  it,  A,  A,  A,  H 

3.  H,  ii  H,  H,  A 

4.  ii  fi  M,  M,  H 

5.  If,  J^,  f§,  if,  U 

Note. — Pupils  should  now  receive  much  practice  in  addition, 
subtraction,  and  division  of  fractions,  basing  the  work  on  the 
principle  previously  developed. 

Fractions  must  be  changed  to  the  same  measure  or  denomina- 
tion before  they  can  be  added,  subtracted,  or  divided.  Occa- 
sionally call  for  a  drawing  to  illustrate  a  given  problem. 


ADDITION  OF  FRACTIONS. 


373.  1.  Add  I  and  |. 


2X4^  8_ 
^2 


3X4 
3X3 
4X3' 


All  answers  must  be  changed  to  their  simplest  form. 


ADDITION  OF  FRACTIONS,  213 

Find  the  sum  of: 


2.1,     i. 

5.  f,    h 

3.  h    |. 

6.  i,    i. 

4.  h     h 

h 

7.  h    f , 

274.  To  add  mixed  numbers,  add  the  integers  and  the 
fractions  separately  and  combine  the  results. 


Add  2f ,  ^,  3i. 

2|  =  2A 
4i=4rV 
3i  =  3A 

9^|  =  10i 

275.  Find  the  sum 

of: 

1.   ^,     3f,     H. 

4.     4i 

8f, 

lOjJj. 

2.   9f,     3i     5|. 

5.    15A, 

31, 

m. 

3.   8,       5f,     7i. 

6.     7f, 

51, 

12A. 

MENTAL    EXERCISE. 

276.  1.  Mary  bought  f  of  a  yard  of  ribbon  on  Tuesday 
and  i  of  a  yard  on  Wednesday.  How  much  ribbon  did  §he 
buy  all  together? 

2.  Mary  gave  J  of  her  money  to  her  sister,  and  ^  of  it  to 
her  brother.     What  part  of  her  money  did  she  give  away? 

3.  One  lot  contains  |  of  an  acre  and  another  lot  |  of  an 
acre.     How  many  acres  are  there  in  both  lots? 

4.  The  difference  between  two  fractions  is  f .  One  frac- 
tion is  I;  what  is  the  other? 

5.  f+^  +  |  =  ? 


214  FRACTIONS. 

6.  I  needed  2^  feet  of  wire  to  hang  one  Japanese  lantern, 
3J  feet  for  another,  and  2iV  feet  for  another.  How  many 
feet  of  wire  were  needed? 

7.  Si  +  5i+^=? 

8.  3i  +  2|  +  3J=? 

9.  2KH  +  t  =  ? 

EXERCISE. 

277.  1.  By  means  of  drawings,  show  the  sum  of  J 
and  f . 

2.  A  farm  is  divided  into  3  fields.  The  first  contains  8i 
acres,  the  second  12 J  acres,  and  the  third  6§  acres.  How 
many  acres  does  the  farm  contain? 

3.  f  +  f  +  r\=? 

4.  Find  the  sum  of  2J,  4?,  5^  and  2j\. 

5.  If  a  tailor  uses  SJ  yards  for  a  coat,  2^  yards  for  trous- 
ers, and  I  of  a  yard  for  a  vest,  how  many  yards  are  used  in 
all? 

6.  Mrs.  Thomas  made  4  dresses.  For  one  she  used  2f 
yards  of  embroidery;  for  another,  1^  yards;  for  another, 
4|  yards;  for  another,  2§  yards.  How  many  yards  in  all 
did  she  use? 

7.  Wilham  walked  3f  miles  on  Monday,  4^  miles  on 
Tuesday,  and  2f  miles  on  Wednesday.  How  far  did  he 
walk  in  the  three  days? 

8.  29K58f  +  77A=? 

9.  Last  Saturday  Mr.  Ray,  a  coal-dealer,  sold  5f  tons, 
8 A  tons  and  6|  tons  of  coal.     How  many  tons  did  he  sell? 

10.  7i  +  5i  +  8r%  +  6t=? 


SUBTRACTION  OF  FRACTIONS.  215 

SUBTRACTION  OF  FRACTIONS. 

EXERCISE. 

278,  1.  Helen  had  |  of  a  yard  of  ribbon;  she  gave  J  of 
a  yard  to  Eleanor;  what  part  of  a  yard  had  she  left? 

5x1—5 
6X1  — & 
1  X3 a 


She  had  J  of  a  yard  left. 


Subtract: 

2.    §-i  =  ? 

6.    f-!  =  ? 

10. 

H-f=? 

3.    t-i  =  ? 

7.   TV-i  =  ? 

11. 

f-l=? 

4.    f-f  =  ? 

8.    |-4=? 

12. 

«-!=? 

5.  W-i  =  ? 

9.  if-4=? 

13. 

I-|=? 

EXERCISE. 

279.  1.  Mr.  Smith  earns  $15  a  week  and  spends  $7| 
week.     How  much  does  he  save  in  one  week? 

$15=$14t 

m 

He  has  left  $7i 
Subtract : 

5.    89-49tV=? 

i|=?  6.    57-18tV=? 

4.     8-3t  =  ?  7.    52-271  =? 


216  FRACTIONS. 


EXERCISE. 


280.  1.  Mary  had  4J  apples  and  gave  If  apples  to  her 
brother.     How  many  did  she  have  left? 

2i 

3  fourths  of  an  apple  from  2  fourtlis  of  an  apple  cannot  be 
taken.  Take  1  apple  from  the  4  apples,  which  leaves  3  apples. 
This  one  apple  equals  4  fourths  of  an  apple.  4  fourths  of  an 
apple  and  2  fourths  of  an  apple  are  equal  to  6  fourths  of  an  apple. 
3  fourths  from  6  fourths  leave  3  fourths.  One  apple  from  3 
apples  leaves  2  apples.     Mary  has  left  2i  apples. 

Subtract : 

2.  4§  ~2i=?        6.  4J  -2i=?        10.    5i  -  2§  =? 

3.  81  -3J  =  ?        7.  6i  -2§  =  ?        11.  15i  -10tV=? 

4.  4x^-1*  =  ?        8.  5f  -1J=?        12.  lOiV-  3J  =? 

5.  10|  -2t=?        9.  6i^i7-2|=?        13.  24i  -18i  =? 

14.  lOi  -  8J=? 

15.  144  -  9|  =  ? 

16.  25i^-16f=? 

MENTAL  EXERCISE. 

281.  1.  I  bought  groceries  amounting  to  |  of  a  dollar. 
How  much  change  did  I  receive  if  I  gave  the  grocer  J  of  a 
dollar? 

2.  I  pay  tV  of  a  dollar  for  a  book  and  sell  it  for  i  of  a  dol- 
lar.   How  much  do  I  lose? 


SUBTRACTION  OF  FRACTIONS,  217 

3.  f-|  =  ? 

4.  f-*=? 

5.  |-f=-? 

6.  Mary  had  $3^  and  spent  $1|.     How  much  had  she 
left? 

7.  The  sum  of  two  numbers  is  5 J.     One  number  is  2|; 
what  is  the  other? 

8.1-1  =  ?' 

9.  Mrs.  Bush  bought  12  pounds  of  sugar.     She  used  6J 
pounds  in  making  jelly.     How  many  pounds  has  she  left? 

10.  My  mother  gave  me  a  ten-dollar  bill  for  my  birthday 
present.     I  spent  $6f  for  a  hat.     How  much  had  I  left? 


EXERCISE. 

282.  1 .  Mrs.  Jones  owned  3^  lots  near  our  school-house. 
She  sold  li  lots  for  $2,200.     How  many  lots  has  she  left? 

2.  A  piece  of  cloth  contains  18^^  yards.     How  many  yards 
will  be  left  after  13f  yards  are  used? 

3.  Find  the  difference  between  12^  and  23^. 

4.  I  spent  $21|  for  a  table  and  a  chair.     The  chair  cost 
me  $12J.     Find  the  cost  of  the  table. 

5.  A  man  bought  a  horse  for  $50,  and  sold  it  for  $45f . 
Find  the  amount  of  loss. 

6.  I  owe  $6f .     If  I  pay  |  of  a  dollar,  how  much  shall  I 
then  owe? 

7.  If  from   $8^  there  be  taken    $6|,   how    much   will 
remain  ? 

8.  A  table  which  cost  Mr.  Howe  $6.75  was  sold  for  $7^. 
What  was  the  gain? 

9.  What  fraction  added  to  |  will  make  H? 


§18  FRACTIONS, 

EXERCISE. 

383.  1.  A  tailor  bought  8}  yards  of  cloth.  He  sold  Si 
yards  for  a  coat,  |  of  a  yard  for  a  vest  and  2f  yards  for 
trousers.     How  many  yards  had  he  left? 

2.  A  lady  bought  a  pair  of  gloves  for  $lf ,  a  hat  for  $7J, 
and  some  lace  for  $1^.  She  gave  the  clerk  a  twenty-dollar 
gold  piece.     How  much  change  should  she  receive? 

3.  A  coal-dealer  bought  25}  tons  of  coal.  He  sold  4J  tons, 
5J  tons,  6f  tons  and  3J  tons.     How  many  tons  had  he  left? 

4.  A  man  bought  wood  for  $6 J,  hay  for  $9|  and  feed  for 
$7i;  how  much  did  all  cost? 

5.  James  had  a  distance  of  85  miles  to  ride.  He  rode 
31f  miles  on  the  first  day  and  24J  miles  on  the  second  day. 
How  many  miles  has  he  still  to  travel? 

6.  From  $23f  take  the  difference  between  $8i  and  $10f . 

7.  A  grocer  cleared  $10  last  Friday;  $lf  was  cleared  on 
vegetables;  $2 J  on  fruits;  $3f  on  flour;  the  remainder  was 
made  on  small  articles.  How  much  did  he  clear  on  small 
articles? 

8.  From  the  sum  of  10|  and  8}  take  their  difference. 

9.  Take  the  difference  between  31  and  8 J  from  10 J. 

10.  From  the  sum  of  6^  and  3|  take  their  difference. 

11.  A  man  divided  his  property  among  his  five  chiklren, 
giving  J  of  it  to  the  first,  J  to  the  second,  i  to  the  third,  and 
iV  to  the  fourth;  what  part  did  the  fifth  child  receive? 

12.  I  of  my  library  is  history,  tV  poetry,  }  science,  and 
the  remainder  fiction;  what  part  is  fiction? 

13.  A  man  did  J  of  his  work  the  first  day,  J  of  it  the  sec- 
ond day,  and  ^  of  it  the  third  day.  What  part  was  left  to 
do  on  the  fourth  day? 


DIVISION  OF  FRACTIONS, 


219 


DIVISION  OF  FRACTIONS. 
Division  by  a  Fraction. 

EXERCISE. 

284.  1.  To  how  many  children  can  I  give  J  of  an  apple, 
if  I  have  ^  of  an  apple? 

I  can  give  to  as  many  children  as  i  of  an  apple  is  contained 
times  in  i  of  an  apple. 

i  of  an  apple  =  f  of  an  apple. 
I  of  an  apple  -f-  i  of  an  apple  =  2. 

I  can  give  i  of  an  apple  to  each  of  2  children. 

In  the  following  problems,  reduce  the  fractions  to  the 
same  denominator  and  then  divide  the  numerators. 


2.  i 

3.  i 

4.  i 

5.  f 

6.  I 


f  =  ? 
*  =  ? 


7.  l-f 


9.  i 

10.  I 

11.  * 


f  =  ? 


-4  =  ? 


i=? 


12.  f 

13.  |-f  =  ? 

14.  I 

15.  i 

16.  f 


4  " 


EXERCISE. 

285.  1.  A  man  has  2  acres  which  he  wishes  to  divide 
into  lots  of  i  of  an  acre  each.  How  many  lots  will  he  have? 

He  will  have  as  many  lots  as  i  of  an  acre  is  contained  times 
in  2  acres. 

2  acres  =  t  acres. 

f  acres  -j-  i  of  an  acre  =  4. 


He  will  have  4  lots. 


10 

FRACTIONS. 

2. 
3. 
4. 

$3H-$i=?                      5.  2oz.-^|oz.  =  ? 

2  bu.  ^i  bu.  =  ?             6.  10  lb.  ^|lb.  =  ? 

3  qt.  ^f  qt.  =  ?              7.5  apples  -^ |  of  an  apple = ? 

8.  8pt.-^Jpt.  =  ? 

9.  6  acres  ^§  acres=? 

10.  9iii.^iin.  =  ? 


EXERCISE. 

286.  1.  A  woman  bought  2§  pounds  of  candy  to  give 
to  her  nephews.  She  placed  it  in  bags  each  holding  \  of 
a  pound.     Into  how  many  bags  did  she  put  the  candy? 

^  21  pounds=f  pounds=\^  pounds. 

■y^  pounds -i-i  pounds =16. 

She  put  the  candy  into  16  bags. 


2.  $3iH-$i=? 

6.  $3fH-$A  =  ? 

10.  $2i^$J  =  ? 

3.     2f  ^  i=? 

7.    2^4-  1  =? 

11.    2f^  |  =  ? 

4.    3f ^  f=? 

8.    5i^  \   =? 

12.    4i^  f  =  ? 

5.    2i-^  i  =  ? 

9.    5i-^  %  =? 

13.    2f-  §  =  ? 

Division  by  a  Whole  Number. 

EXERCISE. 

287.  1.  At  $2  a  yard,  how  much  velvet  can  be  bought 


with  Hi? 

You  can  get  I  of  a  yard. 


i  =  $t. 


DIVISION  OF  FRACTIONS.  221 

2.  4i  bu.  --2  bu.  =  ?  6.  2i  in.  -3  in.  =  ? 

3.  5f  pt.-3pt.  =  ?  7.  lift.H-5ft.  =  ? 

4.  $2i  -$3-  ?  8.  7-1  bbl.  -^3  lb.  =  ? 

5.  $2f  H-$2  =  ?  9.  51  lb.  -r-7  lb.  =  ? 

EXERCISE. 

388.    1.  At   $3  a  barrel,  how  many  barrels  of  apples 
can  be  bought  for  J  of  a  dollar? 

tpo —    4.         $14.    ^4    —  1^  —  4. 

At  $3  a  barrel,  i  of  a  barrel  can  be  bought  for  $|. 

2.  At  $2  a  pound,  what  part  of  a  pound  of  writing  paper 
can  be  bought  with  $^? 

$2  =:  If. 
Ii-lf=i. 

You  can  buy  ^  of  a  pound. 

3.  $i--S2  =  ?  6.  1 4-5=?  9.     4-2  =  ? 

4.  i-  4=?  7.  i-3=?  10.     1^-5=? 

5.  |-H-  4=?  8.  t^2=?  11.  t'o-3  =  ? 

Division  by  a  Mixed  Number. 

289.  1.  At  $3|  a  bushel,  what  part  of  a  bushel  of  cran- 
berries can  be  bought  for  $2? 

«p,C'   —  T  5   •  ^05    —  qp  6  • 

$J,Q  -  $1,^  =  ig  =  I. 
You  can  buy  f  of  a  bushel. 


222  FRACTIONS, 

2.  I  can  save  $1^  from  my  weekly  earnings.     How  long 
will  it  take  me  to  save  S3|? 

$31  =  $V.  $1^  =  $f . 

$1/  -  $f  =  3. 

It  will  take  me  3  weeks. 

3.  At  $1|  a  gallon,  what  part  of  a  gallon  of  cream  can  be 
bought  with  $§? 

$!=$i^.       Ill  =  $i  =  m. 
m-^%u  =  ii  =  ^^ 

You  can  get  A  of  a  gallon. 
290.  EXERCISE. 


1. 

3  yd. 

-2iyd.= 

? 

6. 

$2§^i 

J3i=? 

2. 

5ft.H 

r6f  ft.  =  ? 

7. 

3J  lb. 

-i-2ilb.=? 

3. 

$3^$5i  =  ? 

8. 

?pt.H 

-5Jpt.  =  ? 

4. 

$li- 

$4i  =  ? 

9. 

«-2i. 

=  ? 

5. 

9ibu 

.^2ibu.= 

=  ? 

10. 

f-lf 

=  ? 

11. 

6  oz.  H-2^  oz.= 

=  ? 

12. 

4f- 

^li=? 

13. 

1- 

3i=? 

14. 

3i- 

v-6i=? 

15. 

3i 

^2i  =  ? 

MENTAL   EXERCISE. 

391.  1. 

f-f=? 

2.  |^f=? 

3.  How  many  pounds  of  butter  can  be  bought  with  |  of  a 
dollar,  if  one  pound  costs  |  of  a  dollar? 

4.  How  many  badges,  each  -^q  of  a  yard  long,  can  be  cut 
from  I  of  a  yard  of  ribbon? 


DIVISION  OF  FRACTIONS.         '  223 

5.  How  many  dozen  oranges,  at  f  of  a  dollar  a  dozen,  can 
I  buy  with  $2? 

6.  f^|  =  ? 

7.  John  earns  J  of  a  dollar  a  day.     How  many  days  will 
it  take  him  to  earn  $8? 

8.  How  many  pounds  of  coffee,  at  |  of  a  dollar  pound, 
can  be  obtained  with  $6? 

9.  One  basket  of  peaches  holds  f  of  a  bushel.     How 
many  baskets  will  hold  4  bushels? 

10.  How  many  tables  can  be  covered  with  5  yards  of 
cloth,  allowing  |  of  a  yard  for  each  table? 

11.  How  many  times  may  |  be  subtracted  from  3? 

12.  Among  how  many  families  can  you  divide  4t  tons 
of  coal,  if  each  family  receives  ir  of  a  ton? 

13.  At  J  of  a  dollar  a  pound,  how  many  pounds  of  butter 
can  be  bought  with  $2^? 

14.  5i^t==? 

15.  How  many  books  can  be  covered  with  2f  yards  of 
canvas,  if  you  allow  4  of  a  yard  for  each  book? 

16.  H^|  =  ? 

17.  A  man  divided  $2f  among  his  children,  giving  each 
child  tV  of  a  dollar.     How  many  children  had  he? 

18.  I  have  $1^  with  which  to  buy  ribbon,  at  |  of  a  dol- 
lar a  yard.     How  many  yards  can  I  buy? 

19.  l|-^i^? 

20.  What  part  of  a  barrel  holding  4  bushels  can  be  filled 
with  1|  bushels? 

21.  2^-2  =  ? 

22.  It  takes  2  bushels  of  wheat  to  sow  a  field.     What  part 
of  the  field  can  be  sown  with  f  of  a  bushel? 

23.  f-6=? 


224  •  FRACTIONS. 

24.  li^4i  =  ? 

25.  2f-3i=? 

26.  2f-H  =  ? 


EXERCISE. 

292.  1.  To  how  many  families  does  a  grocer  sell  6  bush- 
els of  apples,  if  each  family  buys  }  of  a  bushel? 

2.  When  sugar  is  5J  cents  a  pound,  how  many  pounds  can 
be  bought  with  $66? 

3.  13f-^5i  =  ? 

4.  John  earns  $1^  a  day.     How  long  will  it  take  him  to 
earn  $1^? 

5.  How  many  vests,  each  containing  1 J  yards,  can  be  cut 
from  lOJ  yards  of  cloth? 

6.  H^5i=? 

7.  Anthracite   is  worth  $7^  a  ton;   $31^  will  buy  how 
many  tons? 

8.  46-^11^=? 

9.  A  merchant  spent  $13^  for  apples  at  f  of  a  dollar  a 
bushel.     How  many  bushels  did  he  get? 

10.  When  flour  is  $7f  a  barrel,  how  many  barrels  can  be 
bought  with  $62? 

11.  A  farmer  received  $175  for  rye  at  |-  of  a  dollar  a 
bushel.     How  many  bushels  did  he  sell? 

12.  How  many  steps  must  be  taken  in  walking  a  mile,  or 
5280  feet,  if  each  step  is  2^  feet  long? 

13.  A  piece  of  cloth  is  45^  yards  long.     How  many  pieces, 
each  containing  If  yards,  can  be  cut  from  it? 

14.  At  $.08^  a  quart,  how  many  gallons  of  strawberries 
can  be  bought  with  $2^? 


DIVISION  OF  FRACTIONS.  225 

EXERCISE. 
293.  1.  A  boy  earns  $5f  one  month  and  $4|  the  next 
month.     How  many  chairs,  at   $1|  apiece,  could  he  buy 
for  his  mother  with  the  money? 

2.  Add  together  3|  and  2^^^  and  divide  the  sum  by  |. 

3.  Mary  had  7j  yards  of  gingham  and  bought  8^  yards 
more.  How  many  aprons  can  she  cut  from  both  pieces,  if 
each  apron  requires  2 J  yards? 

4.  A  man  bought  12 J  acres  of  land  at  one  time,  and  13| 
acres  adjoining,  at  another  time.  Into  how  many  lots  of 
1|  acres  each  could  he  divide  his  land? 

5.  Jane  spent  the  difference  between  $9  and  $5^/  for  a  hat. 
How  many  such  hats  could  be  bought  with  $14? 

6.  Mr.  Harold  raised  50  bushels  of  wheat.  He  sold  7J 
bushels  and  placed  the  remainder  into  bags,  each  holding  2  J 
bushels.     How  many  bags  were  necessary? 

7.  A  grocer  has  36^  pounds  of  flour  in  1  barrel  and  38 A 
pounds  in  another.  He  decides  to  pack  it  in  sacks  each 
holding  12^  pounds.     How  many  sacks  will  be  necessary? 

8.  A  farmer  had  $86.  He  paid  a  bill  amounting  to 
$24^,  and  with  the  remainder  bought  sugar  at  iV  of  a  dollar 
a  pound.     How  many  pounds  did  he  receive? 

9.  A  skilled  carpenter  earned  $49t%  at  one  time  and  $25^ 
at  another.  How  many  days  did  he  work,  if  he  received  $3 
per  day? 

10.  A  furniture  dealer  had  $170|  and  spent  $40tV  for  bed- 
steads. How  many  chairs,  at  $1^  a  piece,  can  he  buy  with 
the  remainder? 

11.  I  wished  to  buy  cloth  for  a  dress,  at  $3^  a  yard.  My 
mother  gave  me  $7f  and  my  brother,  $8J.  How  many 
yards  could  I  buy  with  my  money? 


226 


FRACTIONS. 


MULTIPLICATION   OF   FRACTIONS. 


294.  1.  How  many  inch  squares  are  there  in  this  figure? 

2.  In  i  of  it?        4.  In  f  of  iti 

3.  In  J  of  it?        5.  In  i  of  it?        7. 
8.  In  t  of  it?        9.  i  of  i  is  what  part  of  the  whole? 

10.  i  of  -J-  is  what  part  of  the  whole? 


6.  In  I  of  it? 
In  1  of  it? 


MULTIPLICATION  OF  FRACTIONS.  227 

11.  iofi=?  14.  iofi=?  17.  |oft=? 

12.  iofi=?  15.  f ofi---?  18.  |ofi=? 

13.  iofi=?  16.  ioft=?  19.  iof i=? 

EXERCISE. 

295.  1.  Mary  divided  |  of  a  yard  of  ribbon  equally 
among  3  girls;  what  part  of  a  yard  did  each  girl  receive? 
Each  girl  received  ^  of  I  of  a  yard,   i  of  f  of  yard=i  of  a  yard. 

2.  If  a  man  mows  f  of  an  acre  in  a  day,  how  much  does  he 
mow  in  ^  of  a  day? 

3.  What  is  the  cost  of  |  of  a  yard  of  flannel,  at  ^  of  a  dol- 
lar a  yard? 

4.  If  silk  is  worth  |  of  a  dollar  a  yard,  what  is  |  of  a  yard 
worth? 

5.  If  a  knife  is  worth  to  of  a  dollar,  and  a  slate  |  as  much, 
what  is  the  slate  worth? 

6.  At  f  of  a  dollar  a  pound,  what  is  i^  of  a  pound  of  tea 
worth? 

7.  fofA=? 

8.  What  is  the  cost  of  f  of  a  gallon  of  milk,  at  S.20  a  gal- 
lon? 

9.  A  man^s  field  contained  90  acres  of  land.  He  planted 
I  of  it  in  corn.     How  many  acres  of  corn  had  he? 

10.  The  cost  of  my  dress  is  f  of  $7^.  Find  the  cost  of  the 
dress. 

11.  A  tailor  used  5t  yards  of  cloth  for  a  suit;  f  of  this 
was  used  for  the  coat.  How  many  yards  of  cloth  were  used 
for  the  coat? 

12.  Four  spellers  are  worth  $.60.  What  part  of  this  are 
3  spellers  worth?    How  much  money? 


228  FRACTIONS. 

13.  Find  the  cost  of  12  pencils,  if  10  pencils  are  worth 
$0.25. 

14.  2J  barrels  of  apples  are  worth  $10.  Find  the  cost  of 
1  barrel. 

2i  barrels  =  |  barrels.  We  wish  to  find  the  cost  of  J  of  a  barrel. 
5  )  $10  =  cost  of  \  barrels. 
$2  —  cost  of  i  of  a  bari^el. 
2 

|4  =  cost  of  1  barrel. 
Or  better: 

f  of  a  barrel  =  |  of  f  barrels. 

4  of  $¥-=  $4. 
One  barrel  will  cost  $4. 

Dividing  5  into  10,  as  shown  above,  is  called  cancellation.  It 
should  be  used  whenever  possible. 

15.  What  is  the  cost  of  1  yard  of  cloth,  if  4^  yards  are 
worth  $9? 

16.  Mr.  Smith  paid  $16  for  2f  tons  of  anthracite.  How 
much  was  it  per  ton? 

17.  What  must  a  dealer  pay  for  1  bushel  of  cranberries, 
if  3i  bushels  are  worth  $6.10? 

18.  I  live  10  blocks  from  the  church.  This  is  2J  times 
my  distance  to  school.     How  far  am  I  from  school? 

19.  Z\  baskets  of  peaches  were  sold  for  $4^.  What  was 
the  selling  price  per  basket? 

20.  I  paid  f  of  a  dollar  for  2^  pounds  of  candy.  How 
much  was  it  per  pound? 

21.  A  man  bequeathed  $7500  to  his  son.  This  was  3f 
times  as  much  as  he  gave  to  his  daughter.  Find  the  daugh- 
ter's share. 

22.  25|^4i=? 

23.  57i^l3J  =  ? 


MULTIPLICATION  OF  FRACTIONS. 


229 


296.  From  the  drawing  answer  the  following,  express- 
ing the  answers  in  the 
simplest  form : 


1.  2 

2.  2 

3.  3 

4.  4 

5.  2 

6.  2 

7.  2 

8.  2 

9.  2 

10.  3 

11.  4 

12.  6 

13.  8 


times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 
times 


i=? 
f=? 

~H? 
I  =  ? 
*=? 

tV=? 
tV=? 


14.  T^X10=? 

15.  AX2=? 

16.  AX2  =  ? 


i%X2=? 
? 


17. 
18. 
19.  AX3  =  ? 


AX  4 


20.  AX3  =  ? 

21.  /jX3  =  ? 

22.  AX2  =  ? 


Multiplication  of  a  Fraction  by  an  Integer  or  a  Mixed 
Number. 


EXERCISE. 

SO?.  1.  If  a  yard  of  cloth  costs  §  of  a  dollar,  what  will  3 
yards  cost? 

Three  yards  cost  $3. 


230  MULTIPLICATION  OF  FRACTIONS, 

2.  At  1^  of  a  dollar  a  yard,  how  much  must  be  paid  for  1^ 
yards  of  ribbon? 

1\  yards  =  t  yards. 

■f  of  i  of  a  dollar  =  i  of  a  dollar. 

1\  yards  cost  i  of  a  dollar. 

3.  fX5=?  7.    IX  6=?  11.  5iX  f=? 

4.  JX6=?  8.  HX  f=?  12.  5JX  |  =  ? 

5.  iX4=?  9.  5iX  i  =  ?  13.  4|X  f  =  ? 

6.  |X9=?  10.  HX16=?  14.     §X15=? 

Make,  in    class,  concrete    problems    from    the    above 
examples. 

Multiplication  of  Integers  and  Mixed  Numbers. 
EXERCISE. 

298.  1.  What  will  3  bushels  of  oranges  cost,  at  $5 J  a 
bushel? 

$5i=$^^  $^^x3  =  $16. 

3  bushels  of  oranges  will  cost  $16. 

Multiply: 


2.  b\    X  8. 

6. 

16  XltV 

10. 

9  X3i 

3.  2tV  X  5. 

7. 

1tVX7. 

11. 

3^X4. 

4.  4i    X  6. 

8. 

10  X5i 

12. 

5  X7i 

5.  12    X  Z\. 

9. 

2^  X16. 

13. 

4gX8. 

MULTIPLICATION  OF  FRACTIONS.  231 

Multiplication  of  a  Mixed  Number  by  a  Mixed  Number. 

EXERCISE. 

299.  1.  What  must  be  paid  for  IJ  pecks  of  English  wal- 
nuts, at  $11-  a  peck? 

li  pecks  =  f  pecks. 

$li  =  If. 

2 

li  pecks  of  English  walnuts  cost  li-i. 

Multiply: 

2.  llbyli  6.  5i   by3f.  10.  2|by5i 

3.  3fbyli  7.  3f   by2i  11.  7iby3f. 

4.  Hbyli  8.  2\   by5i  12.  Ubyli 

5.  If  by  H.  9.  mby4i  13.  6iby4f. 

MENTAL    EXERCISE. 

300.  1.  A  boy  walked  2 1  miles  in  1  hour.     How  far 
can  he  walk,  at  that  rate,  in  10  hours? 

2.  Find  the  value  of  12  bushels  of  corn,  at  f  of  a  dollar  a 
bushel. 

3.  At  $.06i  a  yard,  what  will  7^  yards  of  braid  cost? 

4.  A  boy  is  able  to  read  5j  pages  of  his  book  in  an  hour. 
How  much  can  he  read  in  14  hours? 

5.  At  f  of  a  dollar  a  yard,  what  will  8  yards  of  cloth  cost? 

6.  I  bought  5J  yards  of  cloth  at  |  of  a  dollar  a  yard* 
What  did  I  pay  for  it? 

7.  Find  the  cost  of  2f  pounds  of  sugar,  at  5^  cents  a 
pound. 


232  FRACTIONS. 

8.  What  must  I  pay  for  12  barrels  of  flour,  at  $4^  a  bar- 
rel? 

9.  3|X5i  =  ? 

10.  My  distance  from  the  nearest  grocery  is  3f  squares. 
John  must  walk  li  times  as  far.  How  far  does  John  walk 
to  the  grocery? 

EXERCISE. 

301.  1.  How  many  acres  are  there  in  56  lots,  each  con- 
taining f  of  an  acre? 

2.  2|X5i  =  ? 

3.  4JX3f=? 

4.  22iX3f=? 

5.  Mr.  Smith  had  96  bushels  of  potatoes,  which  he  sold 
for  I  of  a  dollar  a  bushel.  How  much  did  he  receive  for 
them? 

6.  5  men  can  do  a  piece  of  work  in  10|  days.  How  long 
will  it  take  one  man? 

7.  The  distance  from  Indianapolis  to  Chicago  is  192  miles. 
The  distance  to  St.  Louis  is  lH  times  as  great.  How  far  is 
it  from  Indianapolis  to  St.  Louis? 

8.  A  man  travels  12f  miles  a  day.  How  far  will  he  travel 
in  5 J  days? 

MISCELLANEOUS  PROBLEMS. 

EXERCISE. 

302.  1.  Mr.  Jones  took  4^  bushels  of  peaches  to  market 
on  Tuesday,  3|  bushels  on  Thursday,  and  4|  bushels  on 
Saturday.  How  much  did  he  receive,  if  he  sold  them  at 
$li  a  bushel? 


MISCELLANEOUS  PROBLEMS.  233 

2.  John  gathered  1 J  dozen,  f  dozen  and  2^  dozen  of  eggs 
at  different  times.  He  sold  them  at  $.18  a  dozen.  How 
much  did  he  get  for  them? 

3.  A  grocer  bought  a  barrel  of  sugar  holding  190  pounds. 
He  kept  40  pounds  for  his  own  use.  He  sold  the  rest  at 
$.05^  a  pound.     How  much  did  he  receive  for  it? 

4.  Multiply  the  difference  between  36|  and  27|  by  7^. 

5.  Multiply  2|  by  1^,  and  divide  the  product  by  l\. 

6.  Divide  the  product  of  2f  and  8|  by  3|. 

7.  Multiply  lOf  by  9J  and  divide  the  product  by  5J. 

8.  What  must  be  paid  for  10  pairs  of  gloves,  if  one  pair  is 
worth  f  of  S3i? 

9.  I  bought  3f  yards  of  velvet  at  %2\  a  yard,  and  3| 
yards  of  silk  at  $/o  a  yard.     What  was  my  bill? 

10.  I  have  $3|  in  my  purse.  I  spend  \  of  it  for  my  din- 
ner.    How  much  must  I  pay  for  11  such  dinners? 

11.  I  used  4^  yards  of  broadcloth  for  my  skirt  and  2f 
yards  for  my  jacket.  How  much  more  did  the  cloth  of  my 
skirt  cost  than  that  of  the  jacket,  if  the  cloth  is  worth  %2\  a 
yard? 

MENTAL  EXERCISE. 

303.  1.  What  is  meant  by  the  following:  f  of  an  apple; 
f  of  a  cake;  |  of  a  book? 

2.  Change  12f  oranges  to  fifths  of  an  orange; 

2|  apples  to  eighths  of  an  apple. 

3.  How  many  weeks  are  there  in  V  weeks? 

4.  How  many  pecks  in  %^  pecks? 

5.  How  many  cents  in  |  of  a  dollar? 

6.  How  many  inches  in  I  of  a  yard? 


234  FRACTIONS. 

7.  Compare  |  of  a  yard  with  ^  of  a  yard,  by  means  of 
inches. 

8.  Compare  |  of  a  bushel  with  |  of  a  bushel,  by  means  of 
quarts. 

9.  Compare  J  of  a  dollar  with  f  of  a  dollar;  f  of  a  dollar 
with  f  of  a  dollar. 

10.  Show  that  §  and  3^2  are  of  the  same  value. 

11.  I  of  63  is  how  much  greater  than  f  of  42? 

12.  Three  hours  is  what  part  of  a  day?    Five  hours? 

13.  Forty  minutes  is  what  part  of  an  hour? 

14.  A  train  runs  30  miles  an  hour.  How  far  will  it  run  in 
40  minutes? 

15.  In  which  of  the  fractions,  j  and  |,  are  the  parts 
smaller? 

16.  Change  |f  to  its  lowest  terms.  Has  the  size  of  the 
parts  increased  or  decreased?  Has  the  number  of  parts  in- 
creased or  decreased? 

17.  i  of  2  apples  is  what  part  of  one  apple? 

18.  Which  is  greater,  J  of  4  or  J  of  5?  How  much 
greater? 

19.  My  flower  garden  is  f  of  a  rod  long  and  |  of  a  rod 
wide;  how  many  rods  around  it? 

20.  I  drew  a  triangle  which  was  5f  inches  on  one  side, 
41i  inches  on  another,  and  5f  inches  on  another.  How 
many  inches  around  it? 

21.  What  is  the  difference  between  5Vo  and  2|? 

22.  The  sum  of  two  numbers  is  16f .  One  number  is  8f ; 
what  is  the  other? 

23.  f-i=? 

24.  The  difference  between  two  fractions  is  jj.  One  of 
the  fractions  is  ^;  what  is  the  other? 


MISCELLANEOUS  PROBLEMS.  235 

25.  To  how  many  people  can  you  give  5|  barrels  of  flour, 
if  you  give  J  of  a  barrel  to  each  person? 

26.  How  many  badges,  each  tV  of  a  yard  in  length,  can  I 
cut  from  1|  yards  of  ribbon? 

27.  I  wish  to  put  4f  pounds  of  candy  into  eighth-pound 
packages.     How  many  packages  can  I  make? 

28.  If  10  oranges  cost  |  of  a  dollar,  what  will  1  orange 
cost? 

29.  At  $8i  a  yard,  what  will  |  of  a  yard  of  velvet  cost? 

30.  There  are  16^  feet  in  one  rod.  How  many  feet  are 
there  in  5  rods? 

31.  I  of  a  quire  of  paper  made  one  note-book;  how  many 
quires  will  be  used  in  making  40  such  books? 

32.  What  will  10^  pounds  of  sugar  cost,  at  6J  cents  a 
pound? 

33.  2iX5J=?     3iX6i=-? 

34.  Bananas  sell  at  the  rate  of  f  of  a  dozen  for  ^  of  a 
dollar.     At  that  rate,  what  will  60  bananas  cost? 

35.  3  oranges  are  sold  for  a  dime ;  what  must  I  pay  for  2\ 
dozen? 

36.  Horace  earns  $1^  a  day.  In  how  many  days,  at  that 
rate,  can  he  earn  $50? 

37.  Divide  25  by  |  of  3|. 

38.  $8i-$|=? 

39.  A  man  owning  f  of  a  mill  sells  f  of  his  share;  what 
part  of  the  mill  does  he  still  own? 

40.  If  a  jar  holds  |  of  a  gallon  of  fruit,  how  many  jars 
will  be  required  to  hold  6  gallons? 

41.  If  3  pounds  of  coffee  are  sold  for  $1,  what  part  of  3 
pounds  should  be  sold  for  25  cents?  What  part  of  one 
pound? 


236  FRACTIONS. 

42.  A  cake  of  ice  f  of  a  foot  thick  floats  J  of  a  foot  above 
the  water;  what  part  of  a  foot  is  below  the  surface?  How 
many  inches  are  below  the  surface? 

43.  A  boy  bought  |  of  a  bushel  of  chestnuts  for  $2,  and 
sold  them  for  10  cents  a  quart;  how  much  did  he  gain? 

44.  Take  ^  of  a  dollar  from  |  of  a  dollar,  and  with 
the  .remainder  buy  oranges  at  |  of  a  dollar  a  dozen.  How 
many  dozen  can  you  buy? 

45.  A  man  is  42  years  old,  and  ^  of  his  age  is  J  of  the  age 
of  his  son.     How  is  old  his  son? 

46.  3  times  J  of  f  is  how  many  times  |? 

47.  Three-fifths  of  a  ton  of  coal  cost  $6.  What  is  the 
cost  per  ton? 

48.  42  is  4  of  what  number? 

49.  I  of  a  cord  of  wood  was  sold  for  $4.50;  how  much  is 
it  a  cord? 

50.  15  is  4  of  a  number;  what  is  ?-  of  the  same  number? 

51.  If  f  of  a  yard  of  ribbon  cost  25  cents,  what  will  i  of 
a  yard  cost? 

52.  One-eighth  of  a  ton  of  coal  costs  |  of  a  dollar. 
What  will  f  of  a  ton  cost? 

53.  Three-fourths  of  a  yard  of  ribbon  cost  12  cents. 
Find  the  cost  of  3  yards.     . 

54.  Five-sixths  of  a  yard  of  cloth  cost  $2J.  Find  the 
cost  of  2  yards. 

55.  Five-eighths  of  the  cost  of  to-day's  meals  are  ^  of 
$2^.     What  is  the  cost  of  to-day's  meals? 

56.  $24  are  |  of  my  money.  Find  J  of  it,  without  find- 
ing all  of  it. 

57.  $1|  is  the  cost  of  |  of  a  pound  of  tea.  Find  the  cost 
of  i\  of  a  pound,  without  finding  the  cost  of  1  pound. 


MISCELLANEOUS  PROBLEMS.  237 

58.  John  had  48  marbles  in  his  bag,  which  were  |  of  all 
his  marbles.  He  gave  away  \  of  his  marbles.  How  many 
did  he  give  away? 

59.  I  pay  $.09  for  |  of  a  yard  of  ribbon.  How  much 
must  I  pay  for  |  of  a  yard? 

60.  Mr.  Hoover  receives  $.15  for  f  of  a  pound  of  coffee. 
How  much  would  he  receive  for  3^  pounds? 

61.  I  of  a  yard  of  cloth  cost  |  of  a  dollar.  What  will  x^^ 
of  a  yard  cost? 

62.  I  pay  $5^  for  |  of  a  barrel  of  flour.  Find  the  value 
of  4  of  a  barrel. 

63.  A  man  is  63  years  old.  \  of  his  age  is  \  of  the  age  of 
his  son.     How  old  is  the  son? 

64.  \  of  my  money  is  -^  of  yours.  I  have  $24.  How 
much  have  you? 

65.  $20  is  i  of  a  man's  salary.     Find  J  of  his  salary. 

66.  A  man  bought  a  cow  for  $35,  and  4  of  that  sum  was 
\  of  what  he  paid  for  a  horse.  What  did  he  pay  for  the 
horse? 

EXERCISE. 

304.  1.  In  three  pieces  of  carpeting  that  contain  44| 
yards,  39f  yards,  and  53J  yards,  there  are  how  many  yards? 

2.  I  sold  a  horse  for  $185i  and  thereby  lost  $9^.  How 
much  did  the  horse  cost? 

3.  A  miner  digs  16|,  21|,  and  18^  ounces  of  gold.  He 
loses  3f  ounces  in  washing.     How  much  gold  has  he  left? 

4.  Add  219f,  407J  and  328f,  and  from  the  sum  take 
4581. 

5.  A  farmer  sold  two  loads  of  hay,  one  for  $15|  and  the 


238  FRACTIONS. 

other  for  $18i,  and  received  $29^  down;  how  much  is  still 
due? 

6.  From  10^  take  the  difference  between  3J  and  8^. 

7.  Among  how  many  families  can  93i  pounds  of  flour  be 
divided,  if  each  family  gets  6^  pounds? 

8.  At  $5 1  a  cord,  how  many  cords  of  wood  can  be  bought 
with  $72i? 

9.  My  father  gave  me  $5f ,  and  my  mother  $6|.  How 
many  books,  at  %1\  apiece,  could  I  buy  with  the 
money  ? 

10.  I  had  25J  acres  of  land.  After  giving  a  number  of 
acres  to  my  son,  I  sold  the  remainder  for  $225,  at  $22^  per 
acre.     How  many  acres  did  I  give  to  my  son? 

11.  A  man  paid  $63  for  5^  tons  of  coal.  What  was  the 
price  per  ton? 

12.  A  woman  paid  $51J  for  13f  yards  of  satin.  How 
much  was  it  a  yard? 

13.  What  will  one  basket  of  peaches  cost,  if  13^  baskets 
cost  $16K 

14.  I  paid  i  of  $4 J  for  a  plate.  How  many  such  plates 
could  be  bought  with  $20tV? 

15.  A  man  having  $||  spent  i^r  of  it.  How  much  had  he 
left? 

16.  Find  the  value  of  ^  of  f  of  a  sailboat  which  is  worth 
$720. 

17.  I  paid  $626  for  8  lots.  How  much,  at  that  rate,  are 
7  lots  worth? 

18.  Seven  plates  are  worth  $8f .  What  are  9  such  plates 
worth? 

19.  Samuel  walked  |  of  llf  miles.  Thomas  only  trav- 
eled TT  as  far  as  Samuel.     How  far  did  Thomas  walk? 


MISCELLANEOUS  PROBLEMS.  239 

20.  A  lady  had  $35  and  spent  f  of  it  for  a  watch.  How 
much  had  she  left? 

21.  A  grocer  bought  63  gallons  of  oil  and  sold  ^  of  it. 
How  many  gallons  had  he  left? 

22.  Mary  had  $15  and  spent  |  of  it  for  lace.  How  much 
money  had  she  left? 

23.  Mr.  Smith  bought  12  gallons  of  vinegar,  and  used  |  of 
a  gallon.     How  many  gallons  were  left? 

24.  Divide  A  of  3f  by  |  of  3i 

25.  From  240  acres  of  land,  43f  acres  are  sold  to  one  man, 
and  J  of  the  remainder  to  another.  How  many  acres  re- 
main unsold? 

26.  If  9i  tons  of  hay  cost  $95,  how  many  tons  can  be 
bought  for  $120? 

27.  28fXl3H-? 

28.  13|  +  19K11§  +  18H? 

29.  At  the  rate  of  9J  miles  an  hour,  how  far  can  a  boy 
travel  on  a  bicycle,  riding  3tV  hours  in  the  forenoon  and  2f 
hours  in  the  afternoon? 

30.  Bought  47  yards  of  cloth;  kept  8^  yards,  and  sold 
the  remainder  at  $3  a  yard.     What  did  I  get  for  it? 

31.  13tX6i^l6f=? 

32.  H-^2fX8H=? 

33.  Multiply  li  -21  by  f  -4i. 

34.  Find  the  value  of  |  of  2|--  (1|-|). 

35.  What  is  the  value  of  f  of  U  -i  of  5i? 

36.  How  many  weeks  will  it  take  to  spend  $182,  if  my 
weekly  expenses  are  $22f  ?  If  my  income  is  $37^  a  week, 
how  much  do  I  save  in  that  time? 

37.  13fX4J^18f  =  ? 


240  FRACTIONS. 

38.  If  a  man  travels  630  miles  in  SJ  days,  how  far  would 
he  travel  in  5^2  days,  at  the  same  rate? 

39.  The  value  of  |  of  a  farm  is  $4,746.  Find  value  of  the 
whole  farm. 

The  value  of  1  of  the  farm  =  $4,746. 

The  value  of  all  of  the  farm  =  $4,746  x  f  =  $5424. 

40.  I  own  I  of  a  store.  I  sell  |  of  my  share  for  $120. 
Find  the  value  of  the  store. 

41.  How  much  cloth  can  be  bought  for  $27,  if  J  of  a  yard 
cost  $2|? 

42.  A  man  drives  45  miles  in  4J  hours.  At  that  rate, 
how  long  will  it  take  him  to  drive  75  miles? 

43.  A  man  receives  $100  for  5|  w^eeks^  labor.  How 
much  should  he  receive  for  working  8f  weeks? 

44.  4§Xl4i-3i=? 

45.  Mr.  Harrow  sold  f  of  his  land  and  had  104  acres  left. 
How  many  acres  had  he  at  first? 

46.  A  boy  used  |  of  the  nails  in  a  paper  bag,  and  found 
on  counting  them  that  the  bag  still  contained  553  nails. 
How  many  were  in  the  bag  at  first? 

47.  I  spent  I  and  |  of  my  money  and  had  $220  left. 
How  much  had  I  at  first? 

48.  After  spending  ^,  f ,  and  |  of  my  money,  I  had 
$783  left;  how  much  had  I  at  first? 

49.  I  withdrew  |  of  my  money  from  bank,  leaving  $725. 
How  much  did  I  withdraw? 

50.  I  had  a  certain  distance  to  walk.  I  walked  J  of  it  in 
the  morning,  ^  of  it  in  the  afternoon  and  the  rest,  which 
was  5  miles,  in  the  evening.    How  far  did  I  walk  all  together? 

51.  Mr.  Atwood  sold  J  of  his  farm  at  one  time,  J  of  it  at 


MISCELLANEOUS  PROBLEMS.  241 

another,  \  of  it  at  another,  and  had  53  acres  left.     How 
many  acres  did  he  sell  in  all? 

52.  Mary  had  224  beads.  This  was  \  more  than  Jane 
had.     How  many  had  Jane? 

53.  Mr.  Holman  sold  a  piece  of  furniture  for  $50.80, 
gaining  ^  of  the  cost.     What  did  it  cost  him? 

54.  Mr.  Smith  has  property  valued  at  $1600.  |  of  this 
is  J  of  the  value  of  Mr.  Joneses  property.  How  much  is 
Mr.  Jones's  property  worth? 

55.  My  father's  farm  produced  625  bushels  of  wheat;  J 
of  this  is  I  of  what  our  neighbor  raised  on  his  farm.  How 
many  bushels  did  our  neighbor  raise? 

56.  I  paid  $8.75  for  |  of  a  ton  of  anthracite.  The  next 
month  I  bought  |  of  a  ton.  How  much  did  I  have  to  pay 
the  second  time,  at  the  same  rate? 


CHAPTER  VIII. 
DECIMAL   FRACTIONS. 


305.     How 

many  rows  are 
there  in  this 
square? 

One  row  is 
what  part  of  the 
whole  ?  Write 
the  fraction 
which  expresses 
this.  What  is 
the  denomina- 
tor? AVhat  is 
the  numerator? 


^  of  anything  may  also  be  written  .1. 

$.1  is  one  way  of  writing  xV  of  a  dollar,  or  $rV,  which  is 
one  dime. 

$.10  may  be  read  as  ^^one  dime  and  no  cents,"  and  has  the 
same  value  as  $.1,  for  both  are  A  of  a  dollar. 

In  this  way  of  writing  fractions,  removing  the  cipher 
from  the  right  does  not  change  the  value.  Express  -^  in 
another  way.    (.2.) 

Express  in  the  same  way  ^,  i^,  i%,  y^. 


DECIMAL  FRACTIONS.  243 

306.  Two  rows  of  this  square  are  what  part  of  the 
whole  square? 

Show  another  way  of  expressing  this  same  fraction. 

Two  rows  are  also  what  part  of  10  rows?     (i.) 

Give  three  ways  in  which  you  may  express  the  relation  of 
2  rows  to  the  whole  square. 

The  first  place  to  the  right  of  the  decimal  point  expresses 
rows  of  the  square,  or  tenths  of  the  square. 

Note. — Have  the  class  work  with  4  rows,  5  rows,  6  rows,  8 
rows,  and  10  rows. 

307.  How  many  squares  are  there  in  each  row? 
How  many  squares  are  there  in  the  large  square? 
One  small  square  is  what  part  of  the  whole  square? 
What  is  the  denominator? 

What  is  the  numerator? 

How  would  you  express  to  o  of  a  dollar?  (1  cent  or  $.01.) 
ito  of  a  dollar?    y^u  of  a  dollar?    I'oi)  of  a  dollar? 

Compare  .1  of  a  dollar  and  .10  of  a  dollar. 

What  is  another  way  of  expressing  too  of  a  dollar?  r|o 
of  anything? 

.01  of  the  whole  square  is  how  many  small  squares?  .03 
of  the  whole  square?     .09  of  the  whole  square? 

308.  Fractions  whose  denominators  are  1  with  zeros 
annexed  are  called  Decimal  Fractions.  rV,  ih^  and  to  oo 
are  decimal  fractions.  The  denominator  of  a  decimal  frac- 
tion is  usually  not  written,  but  the  idea  is  expressed  by 
the  numerator  and  the  decimal  point.  The  usual  form  of 
writing  the  decimal  fractions  given  above  is  :  .1,  .03  and 
.0011. 

Decimal  is  from  a  Latin  word  meaning  ten. 


244  DECIMAL  FRACTIONS. 

309.  Fractions  whose  denominators  are  not  1  with  ciphers 
annexed  are  called  Common  Fractions,  f ,  I,  H;  and  ^^ 
are  common  fractions. 

310.  Ten  squares  are  what  part  of  the  whole  square? 

(iWr.) 

Express  this  fraction  as  a  decimal. 

Ten  small  squares  are  the  same  as  what?     (1  row.) 

We  know  that  1  row  is  what  part  of  the  whole  square? 

Show  the  four  ways  in  which  you  may  express  the  relation 
of  10  small  squares  to  the  whole  square. 

311.  Twenty-five  small  squares  are  what  part  of  the 
whole  square? 

Express  it  decimally. 

Twenty-five  small  squares  are  how  many  rows? 
2J  rows  are  what  part  of  the  whole?     (.2^  or  {.) 
Give  four  ways  of  expressing  the  value  of  25  squares. 
WTr=.25  =  .2i  =  i) 

Note. — Have  the  class  work  with  50  squares,  75  squares,  100 
squares. 

312.  One  row  of  squares  is  what  part  of  the  whole?  (.1.) 
One  small  square  is  what  part  of  the  whole?     (.01.) 

One  row  and  one  small  square  is  what  part  of  the  whole? 

(.11.) 

Compare  the  value  of  the  figure  in  the  second  place  to  the 
right  of  the  decimal  point  with  that  of  the  figure  in  the  first 
place  to  the  right  of  the  decimal  point,  describing  them  as 
parts  of  the  square.  (1  row  =  10  small  squares;  1  small 
square  is  tV  of  10  small  squares.) 


DECIMAL  FRACTIONS.  245 

Compare  the  value  of  the  number  in  the  second  decimal 
place  with  that  of  the  number  in  the  first  decimal  place. 
(.1  =  .10;  .01  =  iV  of  .1.) 


Fundamental  Processes. 

Note. — The  class  should  review  work  showing  the  processes 
which  may  be  performed  with  like  numbers  ;  also  the  work 
showing  that  the  processes  of  addition,  subtraction,  division  and 
comparison  may  sometimes  be  performed  with  unlike  numbers ; 
as  6  bushels  and  2  pecks.     (§  257.) 

313.  Add,  subtract,  divide,  and  compare  .6  and  .2,  in 
the  language  of  the  square. 

6  rows  and  2  rows  =  8  rows. 

6  rows  less  2  rows  =  4  rows. 

6  rows  -T-  2  rows  =  3  (times). 

2  rows  =  i  of  6  rows. 

6  rows  are  4  rows  more  than  2  rows. 

2  rows  are  4  rows  less  than  6  rows. 

Perform  these  processes  in  the  language  of  United  States 
money. 

Add,  subtract,  divide,  and  compare  .6  and  .2,  as  decimal 
fractions. 

314.  Add,  subtract,  divide  and  compare  .6  and  .15  in 
the  same  manner  as  shown  in  §  313. 

6  rows  =  60  small  squares. 
60  small  squares  and  15  small  squares  =  75  squares. 

6  dimes  =  60  cents. 

60  cents  +  15  cents  =  75  cents. 


246  DECIMAL  FRACTIONS. 

Name  the  least  number  of  coins  you  can  have  when  you  have 
75  cents.     What  other  coins  taken  together  will  make  75  cents  ? 

6  tenths  =  60  hundredths. 
60  +  15  =  75. 

Note. — The  teacher  should  make  original  problems. 


WRITING  AND  READING  DECIMALS. 

315.  Can  you  imagine  an  oblong  that  is  100  inches  long 
and  10  inches  wide? 

Note. — This  could  be  drawn  on  the  blackboard — 10  inches 
high,  100  inches  long. 

How  many  one-inch  squares  would  there  be  in  this  ob- 
long?    (1000.) 

One  one-inch  square  is  what  part  of  the  oblong? 

Express  this  decimally. 

What  is  the  denominator?    What  is  the  numerator? 

If  a  dollar  sign  were  placed  in  front  of  this,  in  what  two 
ways  might  it  be  read?  (One  thousandth  of  a  dollar  or  1 
tenth  of  a  cent.) 

316.  Ten  one-inch  squares  are  what  part  of  the  oblong? 

u  000-; 
Ten  one-inch  squares  are  the  same  as  what?     (1  row.) 
One  row  is  what  part  of  the  oblong?     ( rko  or  .01 .) 
Give  the  four  ways  of  expressing  the  value  of  10  one- 
inch  squares. 

317.  Five  hundred  one-inch  squares  are  what  part  of 
the  whole?     dVA  or  .500.) 


REDUCTION. 


247 


Five  hundred  one-inch  squares  are  what  part  of  the  1000 
one-inch  squares?     (J.) 

Five  hundred  one-inch  squares  are  the  same  as  how- 
many  rows? 

Fifty  rows  are  what  part  of  the  oblong?     {-f^^  or  .50.) 

Give  five  or  more  ways  of  expressing  the  relation  of  500 
one-inch  squares  to  the  1000  one-inch  squares. 

318.  Express  the  following  in  decimal  form: 

tV  tV,  i¥o,  tVo,  t¥A,  iVA,  6A,  25t*o,  36rAo. 

6  hundredths.     19  hundredths.       60  thousandths. 
25  hundredths.     40  thousandths.       9  and  7  tenths. 
301  thousandths.  97  hundredths.         6  and  7  hundredths. 

Read  the  following  decimals : 


.5 

.06 

.145 

3.45 

.700 

.05 

.60 

.265 

4.89 

4.900 

.15 

.56 

.103 

5.07 

4.009 

.30 

.84 

.047 

7.008 

6.800 

,45 

.96 

.006 

9.037 

6.080 

REDUCTION. 

To  change  Decimals  to  Common  Fractions. 

319.  Change  .6  to  a  common  fraction  in  lowest  terms, 
having  the  same  value. 

To  change  a  decimal  to  a  common  fraction,  write  the  de- 
nominator under  the  decimal ^  omit  the  decimal  point,  and 
change  the  fraction  to  its  lowest  terms. 


248  DECIMAL  FRACTIONS. 


EXERCISE. 

330.  Change  to  equivalent  common  fractions  or  mixed 
numbers: 


1. 

.8. 

8. 

.015. 

2. 

.75. 

9. 

.275. 

3. 

.9. 

10. 

.048. 

4. 

.60. 

11. 

.009. 

5. 

.625. 

12. 

5.36. 

6. 

.35. 

13. 

3.25. 

7. 

.15. 

14. 

15.75. 

To  Change  Common  Fractions  to  Decimals. 


1 331.  1.  Drawa 

line  and  divide  it  into  halves.    Express  the  divided  line 
fractionally,     (f.) 

1 ' 1 1 — -I 1 1 1 ' 2.  Draw  a  line 

and  divide  it  into  10  equal  parts.    Express  it  fractionally. 
(U  or  1.0.) 

3.  Imagine  the  line  cut  into  100  equal  parts;  express  it 
fractionally.     (iU  or  1.00.) 

We  see  that  1  =  1.0  or  1.00  or  1.000,  etc. 

4.  Express  5  as  tenths,  hundredths,  thousandths.     (5  = 
5.0  or  5.00  or  5.000.) 

5.  Express i decimally.     (Jof Horjof  1.0  =  .5.     i=.5.) 

6.  Express  i  decimally,     (i  of  1.000  =  .125.) 

7.  Express  f  decimally.     (|  of  1.00  =  .75;  or  i  of  3.00= 
.75.) 


ADDITION  OF  DECIMALS. 


249 


To  change  a  common  fraction  to  a  decimal,  express  the 
numerator  decimally  and  divide  by  the  denominator. 


EXERCISE. 


322,  Change  to  equivalent  decimals: 


1. 

i. 

2. 

i- 

3. 

1- 

4. 

f. 

5. 

i- 

6. 

I. 

7. 

h 

8.  I 

9.  I. 

10.  I 

11.  i 

12.  f . 

13.  i 

14.  A. 


15.  if. 

16.  A. 

17.  3i. 

18.  7|. 

19.  12i^. 

20.  ^2^, 

21.  26f. 


ADDITION  OF  DECIMALS. 

Note. — Eeview  addition  as  given  in  §  313  and  §  314. 

3«3.  6  tenths +  15  hundredths  =? 

6  tenths  =  60  hundredths- 
.60+  .15  =  .75 
or 

.60 

.75 

Find  the  sum  of  25.4,  120.7,  216.009,  and  .496. 

25.4 

1*^^^'7  Write  the  numbers  so  that  units  of  the  same  order 

216.009       stand  in  the  same  column.     Begin  at  the  right  and 
.496       ^^^  ^^  ^^  addition  of  integers. 

362.605 


250  DECIMAL  FRACTIONS. 

EXERCISE. 

324.  Find  the  sum  of: 

1.  .680,  .729,  .006,  .3,  .40,  and  .400. 

2.  65.789,  36.908,  45.8,  and  3001.601. 

3.  8.675,  34.604,  .007,  .897,  and  189.3. 

4.  1009.09,  3040.60,  10001.345,  .009,  and  987. 

5.  62.5  yards +  95.7  yards  f  67.25  yards +  9.48  yards. 

6.  9  and  101  thousandths,  7  and  3  tenths,  15  and  75 
hundredths,  38  and  25  thousandths. 

7.  One  hundred  eleven  thousandths,  two  hundred 
twenty-five  thousandths,  sixteen  tenths,  one  hundred  five 
and  one  hundred  five  thousandths,  three  hundred  fifty  and 
three  hundred  thousandths. 

8.  Add  as  decimals:  56i  49 A,  42^,  39i  15 J. 

SUBTRACTION  OF  DECIMALS. 

Note. — Keview  subtraction  as  given  in  §313  and  §314. 

325.  From  .04  take  .005. 

.4  =  .400        .400  -  .005  =  .395. 
or 

.400 
.005 
.395 

From  45.75  take  26.9. 

40. /o  Write  the  subtrahend  under  the  minuend,  so  that 

26.9         units  of  the  same  order  shall  stand  in  the  same  column, 


18.85 


and  subtract  as  in  the  subtraction  of  integers. 


DIVISION  OF  DECIMALS.  251 

From  64.7  take  19.013. 

64.700  If  there  are  more  decimal  places  in  the  subtrahend 
19  01 S  than  in  the  minuend,  fill  the  vacant  decimal  orders  of 
the  minuend  with  ciphers. 

EXERCISE. 

326.  Find  the  difference  between: 

1.  303.48  and  199.09. 

2.  87.076  and  65.005. 

3.  1005.15  and  105.015. 

4.  .8  and  .08. 

5.  9  tenths  and  9  thousandths. 

6.  101.009  and  81.998. 

7.  1616.161  and  987.90. 

8.  7  hundredths  and  7  thousandths. 

9.  90  hundredths  and  90  thousandths. 

10.  From  80  thousand  and  80  thousandths  take  8  thous- 
and and  8  thousandths. 

11.  Find  the  difference  between  seven  and  seven  tenths, 
and  seven  and  seven  thousandths. 

12.  A  man  walked  42.5  miles  the  first  day  and  17.875 
miles  the  second.  How  much  farther  did  he  walk  the  first 
day  than  the  second? 

DIVISION  OF  DECIMALS. 

Note. — Review  division  as  given  in  §  313  and  §  314. 

EXERCISE. 

327.  1.  At  $15  apiece,  how  many  books  may  be  bought 
with  6  dimes? 


252  DECIMAL  FRACTIONS. 


6  dimes  =  60  cents. 

60  cents  -t- 15  cents 

=  4. 

You  can  get  4  books. 

2.  $.8  ^$.02  =  ?                        8. 

$5.5 -=-$.25  =  ? 

3.  $.02  ^$.005  =  ?                    9. 

$2.1  ^$.35  =  ? 

4.  15  acres -J- .5  acres  =?         10. 

15.3  gal. -^5.1  gal.  =  ? 

5.  $2  ^$.05  =  ?                       11. 

$4.6  ^$1.15=? 

6.  5bu.-^2.5bu.  =  ?                12. 

$.5^$.00J  =  ? 

7.  8peeksH-1.6pecks=?       13. 

$3.8  ^$.76=? 

EXERCISE. 

328.  1.  What  part  of  a  gallon  of  milk  can  be  bought 
with  $.04,  if  milk  sells  for  .2  of  a  dollar  per  gallon? 

.2  of  a  dollar  =  20  cents. 
4  cents  -t-  20  cents  =  ^  =  i  =  .2. 
or 

$.04  ^  $.2  =  $.04  H-  $.20  =  .2. 

.2  of  a  gallon  of  milk  can  be  bought  for  $.04. 

2.  $.08-T-$.4=? 

$.08  H-  $.4  =  $.08  ^  $.40  =  -/o  =  ^  =  .2. 

3.  .04 -.2=?  5.  $.4 ^$.2=? 

4.  .5^2.5=?  6.  .63^4.5=? 

.63  -^  4.5  =  .63  -J-  4.50  =  -,%%  =  /o  =  S7  =  -l^. 

7.  25  bushels -5  bushels=  ?  11.  $1.2  -$24=  ? 

8.  2  pints -25  pints=?  12.  2-2.5=? 

9.  $1.5 -$2.5=  ?  13.  1.2-2.4=? 
10.  2.04-25.5=?  14.  3.6^7.2=? 


DIVISION  OF  DECIMALS.  253 

EXERCISE. 

329.  1.  A  man  earns  .2  of  a  dollar  in  one  hour.     In 
how  many  hours  can  he  earn  .5  of  a  dollar? 

.  5  of  a  dollar  -^  .2  of  a  dollar  =  2h 

2i  =  2.5. 

It  will  take  him  2. 5  hours. 

2.  .9-^.4=? 

.9-i-  A  =  I  =2i  =  2.25. 


3.  .7- 

-  .5=?        7.       9   -^3.6  =?       11.  16.8^3.5=? 

4.    2- 

-  .8=?        8.  1.25   ^  .5  =?        12.  15.5-^5    =? 

5.    5- 

-    4=?        9.  3.125^  .25  =  ?       13.  36.4^8    =? 

6.16- 

-2.5=?      10.  6.25   ^2.5  =?        14.  29.7-^9    =? 

330.  1.  Divide  16.048  by  3.4.       2.  Divide  9.5  by  .25. 

3.4)16.048(4.72                   .25(9.50(38 

13  6                                          7  5 

2  44                                        2  00 

2  38                                        2  00 

68       •  9.5  =  950  hundredths  -f-  25    hun- 

68  dredths  =  38,  an  integral  number. 

Divide  as  in  the  division  of  integers,  and  point  off  as  many 
decimal  places  in  the  quotient  as  the  number  of  decimal  places 
in  the  dividend  exceeds  the  number  in  the  divisor. 

1.  When  the  dividend  has  fewer  decimal  places  than  the  divi- 
sor, annex  ciphers  to  the  dividend. 

2.  When  the  quotient  has  not  enough  decimal  figures,  prefix 
ciphers. 

3.  When  there  is  a  remainder,  the  division  may  be  continued 
by  annexing  ciphers  to  the  dividend. 


254  DECIMAL  FRACTIONS. 

EXERCISE. 

331.  1.  I  have  $.72  with  which  to  buy  starch  at  $.045  a 
pound.     How  many  pounds  can  I  buy? 

2.  A  candy  dealer  has  35  pounds  of  candy  to  place  in 
bags,  each  holding  .875  of  a  pound.  How  many  bags  will 
be  needed? 

3.  Mr.  Brown  bought  60  acres  of  land  and  divided  it  into 
lots,  each  containing  .75  of  an  acre.  How  many  lots  does 
he  have? 

4.  A  furniture  dealer  has  $330  with  which  to  buy  chairs 
at  $7.5  apiece.     How  many  chairs  can  he  buy? 

5.  Flannel  sells  for  .625  of  a  dollar  per  yard.  At  that 
rate,  how  many  yards  could  I  buy  with  $11.25? 

6.  A  man  who  owns  a  paper  stand  makes  $16.35  per 
week.  How  many  papers  does  he  sell  in  a  week  if  he  makes 
.0025  of  a  dollar  on  each  paper? 

7.  .0007-^.45=? 

8.  At  $9,875  an  acre,  how  many  acres  of  land  would  I  re- 
ceive for  $63.99? 

Divide : 

9.  34.5  by  .15. 

10.  34.5  by  .015. 

11.  5.5  by  1.25. 

12.  5.5  by  .0125. 

13.  450.5  by  1.75. 

EXERCISE. 

332.  1.  One-half  of  $6=?  One-half  of  6  cents  =  ?  Of 
.06=?    Of  .006=? 


DIVISION  OF  DECIMALS.  255 

2.  A  man  divided  .16  of  a  square  mile  of  land  between  2 
men.    What  part  of  a  square  mile  did  each  receive? 

2  ).  16  of  a  square  mile. 
.08  of  a  square  mile. 

Each  man  received  .08  of  a  square  mile. 

3.  Mr.  Smith  bought  .625  of  an  acre  of  land.  He  divided 
it  so  as  to  have  5  equal  garden  plots.  What  part  of  an  acre 
did  each  plot  contain? 

4.  I  paid  $.75  for  4  yards  of  ribbon.  How  much  was  it 
per  yard? 

5.  Eight  bushels  of  peaches  sell  for  $6.  How  much  are 
they  per  bushel? 

6.  I  paid  $.09  for  .3  of  a  yard  of  embroidery.  How  much 
was  it  a  yard? 

3 )  $.09  =  cost  of  .3  of  a  yard. 
$.03  =  cost  of  .1  of  a  yard. 

10  (10  times  .1=1). 
$.30  =  cost  of  1  yard. 

7.  $.80  is  the  cost  of  .25  of  a  yard  of  silk.  Find  the  cost 
of  a  yard. 

8.  Eighteen  cents  are  .9  of  what  I  paid  for  some  tablets. 
What  did  I  pay  for  them? 

9.  .8  of  a  gallon  of  cream  cost  $.30.  How  much  does  a 
gallon  cost? 

10.  I  paid  $.50  for  2.5  yards  of  ribbon.  Find  the  cost  of 
1  yard. 

2. 5)  $.500,  cost  of  2.5  yards. 
$.20,  cost  of  1  yard. 


256 


DECIMAL  FRACTIONS. 


11.  I  paid  $.70  for  3.5  pounds  of  porterhouse  steak. 
How  much  did  I  pay  for  one  pound? 

12.  4.8  yards  of  shirt-waist  material  cost  me  $1.44.  How 
much  was  it  per  yard? 

13.  I  paid  $99  for  4.4  acres  of  land.  How  much  did  I 
pay  for  one  acre? 

14.  Mr.  Berry  bought  a  farm  for  $1200  and  sold  it  so  as 
to  gain  25^  of  the  cost.     What  was  his  gain? 

15.  Our  neighbor  receives  a  salary  of  $1500  per  year. 
He  pays  33^^  of  this  for  house  rent.  How  much  money 
has  he  left  after  paying  his  rent? 

MULTIPLICATION  OF  DECIMALS. 


Note. — Introduce  this  work  by  means  of  one  hundred  one- 
inch  squares,  supplemented  by  United  States  money. 

333.  1.2  times 
1  row=? 

2. 1  row  is  what 
part  of  the  whole? 

3.  2  times  .1  =  ? 

4. 10times.l  =  ? 

5.  5  times  .2  =  ? 

6.5  times  4 
rows=? 

7.  5  times  .4=? 

8.  8  times  .4=? 

9.  9  times  .5=? 
10.2.5times.4=? 
11.5.5times.8=? 
12.2.2times.5=? 


MULTIPLICATION  OF  DECIMALS.  257 

13.  4  times  1  small  square  =  ? 

14.  1  small  square  is  what  part  of  the  whole? 

15.  .01X4=?  17.  .10X10=?  19.  5.5X10=? 

16.  .02X4=?  18.  4.5X10=?         20.  6.5X10=? 

EXERCISE. 

334.  1.  2  times  2.1  =  ?  5.  4.8X3=? 

2.  5.2X3  =  ?  6.  2.5X2=? 

3.  5.3X6  =  ?  7.  4.2X10=? 

4.  4.6X5=?  8.  8.1X5  =  ? 

EXERCISE. 

335,  1.  Multiply  .253  by  .35. 

.253  Multiply  as  in  whole  numbers,  and  point  off  as 

35  many  decimal  places  in  the  product  as  there  are  in 
both  multiplicand  and  multiplier.  If  there  are  not 
enough  figures  in  the  product  to  fill  the  decimal 
places,  prefix  as  many  ciphers  as  are  necessary  to 


1265 
759 


.08855       make  the  required  number. 

Multiply: 

2.  .386  by  .47  6.  49.3  by  .064 

3.  .231  by  .36  7.  492  by   3.8 

4.  48.2  by  25  8.  384.45  by  .64 

5.  48.2  by  .25  9.  38.445  by  .64 

10.  What  is  the  cost  of  26.25  pounds  of  sugar,  at  $.0625 
per  pound? 

11.  One  acre  of  land  produces  48.375  bushels  of  wheat. 
How  many  bushels  will  7.25  acres  produce? 

12.  At  $6.37  a  ton,  what  must  be  paid  for  5.25  tons? 


258  DECIMAL  FRACTIONS, 

MENTAL    EXERCISE. 

336.  1.  Make  decimal  fractions  of  the  following:  ■^\; 

TU'}    12]    lo'WU':    it' 

2.  State  the  numerator  and  the  denominator  of  the  fol- 
lowing: .03;  1.25;  .075;  .0075;  .00205. 

3.  Change  to  common  fractions  in  lowest  terms:  .4;  .05; 
.6;  .12;  .75;  .8;  .24;  .50;  2.5;  .16|. 

4.  Compare  the  values  of: 

.6   andt;        .04   andi; 
.05  and  I ;        .875  and  J. 

5.  Change  to  decimal  fractions: 

il  i'}  4;  il  i')  J  J  A  J  il  i'y  i]  ^s]  /o. 

6.  What  decimal  of  a  pound  do  I  buy  in  buying  J  of  a 
pound  of  coffee? 

7.  A  of  a  foot  is  what  decimal  of  a  foot? 

8.  Change  J  and  f  to  decimals  and  add. 

9.  Add  one  hundredth  and  one  tenth. 

10.  I  paid  f  of  a  dollar  for  a  knife  and  J  of  a  dollar  for  a 
book.    How  many  dollars  and  cents  did  I  spend? 

11.  Add  i  and  i  as  decimals. 

12.  I  and  J  are  equal  to  what  decimal? 

13.  A  boy  spends  .33^  of  a  day  in  sleep  and  ^  of  a  day  in 
study.     What  fractional  part  of  a  day  is  left? 

14.  Subtract  one  hundredth  from  one  tenth. 

15.  A  man  has  10  loads  of  hay  and  sells  .05  of  a  load ; 
how  much  hay  has  he  left? 

16.  From  the  sum  of  4.4  and  .08  take  4.1. 

17.  From  4.4  take  the  difference  between  .04  and  4.1. 

18.  4X.05  is  what  common  fraction? 


MULTIPLICATION  OF  DECIMALS.  259 

19.  One  book  costs  8  hundredths  of  a  dollar.  What  will 
9  such  books  cost?     ($.08 X9  =      .) 

20.  .3X.005-? 

21.  What  is  the  shortest  way  of  multiplying  .48  by  100? 

22.  Change  f  to  a  decimal,  take  away  .01,  and  multiply 
by  100. 

23.  From  1  take  .001,  and  multiply  by  a  thousand. 

24.  I  own  .1  of  a  farm  and  sell  i  of  my  share.  What  dec- 
imal part  of  the  farm  do  I  sell? 

25.  When  apples  are  tV  of  a  dollar  a  bushel,  what  must 
you  pay  for  .7  of  a  bushel? 

26.  Divide  $8  into  400  equal  parts. 

27.  From  1  take  .001  and  multiply  by  100. 

28.  Ten  men  can  do  a  piece  of  work  in  2.1  days.  How 
long  will  it  take  one  man  to  do  it? 

29.  .lof  .01  =  ? 

30.  At  $2  a  yard,  how  much  silk  can  be  bought  with  $.40? 

31.  I  buy  a  cord  of  wood  for  $5  and  sell  it  for  $5.50.  The 
gain  is  what  decimal  part  of  the  cost? 

32.  Multiply  .75  by  10,  and  divide  the  product  by  .03. 

33.  A  man  gained  4  mills,  or  $0,004,  on  a  quart  of 
nuts.     How  many  quarts  must  he  sell  to  gain  $.40? 

34.  What  is  the  quotient  of  .1  divided  by  .01? 

35.  A  grocer  bought  potatoes  at  $.40  a  bushel  and  sold 
them  so  as  to  gain  10^,  or  .10,  of  the  cost.  What  was  the 
gain  on  the  bushel? 

36.  My  watch  cost  me  $60.  I  sold  it  so  as  to  lose  25^, 
or  .25,  of  the  cost.     What  did  I  lose? 


260  DECIMAL  FRACTIONS. 


MISCELLANEOUS  PROBLEMS. 


337.  1.  The  subtrahend  is  eight  thousand  and  forty- 
eight  thousandths,  and  the  remainder  is  eight  hundred 
seventy-three  thousandths;  what  is  the  minuend? 

2.  There  are  228.35  barrels  of  water  in  a  cistern  which 
will  hold  410.5  barrels;  how  many  barrels  will  be  needed  to 
fill  the  cistern? 

3.  At  .085  of  a  dollar  per  dozen,  what  will  lOf  dozen  steel 
pens  cost? 

4.  From  a  barrel  containing  43  gallons  of  vinegar,  .125 
gallons  were  drawn  at  one  time,  3.5  at  another,  and  .75  at 
another;  now  many  gallons  remained  in  the  barrel? 

5.  Dry  goods  valued  at  $8000  were  destroyed  by  fire; 
what  would  a  man  lose  who  owned  .12  of  the  goods? 

6.  A  gallon,  liquid  measure,  contains  231  cubic  inches; 
how  many  gallons  are  there  in  13051.5  cubic  inches? 

7.  At  $6.80  an  acre,  how  many  acres  of  land  can  be 
bought  for  $4258? 

8.  Bought  17  chests  of  tea,  each  containing  59  pounds, 
at  $0.67  a  pound,  and  gave  in  exchange  118  bags  of  wheat, 
each  containing  3.4  bushels;  what  was  the  value  of  the 
wheat  per  bushel? 

9.  When  the  dividend  is  .1  and  the  divisor  12.8,  what  is 
the  quotient? 

10.  What  is  the  quotient  of  312.5  by  85? 

11.  If  38  yards  of  cloth  cost  $180.50,  what  will  be  the  cost 
of  26  yards? 

12.  At  $2.56  per  yard,  how  many  yards  of  cloth  can  be 
bought  for  $94.4? 

13.  From  $62.40  take  $7.37^ 


MISCELLANEOUS  PROBLEMS,  261 

14.  A  druggist  sold  375  gallons  of  ink  in  bottles  holding 
.375  of  a  gallon  each;  how  many  bottles  of  ink  did  he  sell? 

15.  By  selling  a  carriage  for  $195,  I  lost  $34.50.  For 
how  much  should  I  have  sold  it  to  gain  an  amount  equal  to 
.7  of  what  I  lost? 

16.  From  the  sum  of  $15.75  and  $1001.10  take  the  sum 
of  $101,018  and  $50,101. 

17.  Subtract  $.50  from  $1,005. 

18.  A  man  bought  a  coat  for  $16,  a  vest  for  $3.50,  and  a 
pair  of  trousers  for  $5.50;  what  two  coins  will  exactly  pay 
for  them? 

19.  From  the  sum  of  $14.50  and  $12.75  take  6  dimes  6 
mills. 

20.  From  $4.50  take  37i  cents. 

21.  A  grocer  bought  3  barrels  of  apples  for  $6.75,  a  box  of 
lemons  for  $2.50,  and  5  barrels  of  flour  for  $30.00.  He 
handed  the  merchant  two  gold  pieces,  and  received  $.75 
in  change.     What  were  the  two  pieces  of  money? 

22.  At  $.12^  a  yard,  how  much  muslin  can  be  bought  for 
$20.43? 

23.  If  f  of  a  yard  of  cloth  cost  $2.16,  what  will  be  the  cost 
of  5i  pieces,  each  containing  47  yards? 

24.  When  rice  is  selling  at  $.075  a  pound,  how  many 
pounds  can  be  bought  for  $5.25? 

25.  How  many  days,  of  9  hours  each,  must  a  man  work 
in  order  to  earn  $576.72,  at  18  cents  an  hour? 

26.  If  a  lady  earns  $15.00  a  week,  and  spends  an  average 
amount  of  $11.37^,  in  how  many  weeks  will  she  save 
$166.75? 

27.  31.5  gallons  of  vinegar  cost  $11.81^;  how  much  is 
that  per  gallon? 


CHAPTER  IX. 

COMPOUND  NUMBERS. 

Note. — Only  so  much  of  Compound  Numbers  should  be  used 
as  seems  to  be  adapted  to  the  age  and  development  of  the  pupils. 

338.  A  Simple  Quantity  is  expressed  in  units  of  one  de- 
nomination; as  4  pecks. 

A  Compound  Quantity  is  expressed  in  units  of  different 
denominations  which  may  be  reduced  to  units  of  the  same 
denomination;  as  4  pecks,  3  quarts. 

339.  A  Denominate  Number  is  a  number  composed  of 
denominate  units. 

A  Simple  Denominate  Nimaber  is  composed  of  units  of  one 
denomination;  as  5  gal.  or  13  bu. 

A  Compoimd  Denominate  Number  is  composed  of  units 
of  two  or  more  denominations  which  may  be  reduced  to 
units  of  the  same  denomination;  as  4  lb.  9  oz. 

340.  Reduction  is  the  process  of  changing  the  denomi- 
nation of  a  number  without  changing  its  value. 

In  reducing  denominate  numbers,  the  increase  or  decrease  in 
the  number  of  units  is  irregular,  instead  of  by  ten  as  in  simple 
numbers. 

DRY  MEASURE. 

341.  Dry  measure  is  used  in  measuring  grain,  fruit, 
seeds,  vegetables,  and  other  dry  articles. 


DRY  MEASURE.  263 

The  denominations  are  'pintSj  quarts,  pecks,  and  bushels. 

2  pints  (pt.)  =  1  quart  (qt.). 
8  quarts         =  1  peck  (pk.). 
4  pecks  =  1  bushel  (bu.). 

1  bu.  =  32  qt.  =  64  pt. 

The  standard  bushel  is  18i  inches  in  diameter  and  8  inches 
deep,  and  contains  2150.42  cubic  inches. 

1.  How  many  bushels  in  24  pecks?     In  25  pecks?     In 
35  pecks? 

2.  Reduce  5  bushels  to  pecks.     To  quarts. 

3.  Reduce  2  pecks  to  pints.     2  bushels  to  pints. 

342.  Reduce  16  bu.  3  pk.  1  pt.  to  pints. 

bu.    pk.    qt.    pt.         One  bushel  =  4  pecks.     In  16  bushels  there 
16     3     0     1     are  4  times  as  many  ones  of  pecks  as  ones  of 
4  bushels.     16  multiplied  by  4  =  64.     There  are 

~     ,  64  pecks  in  16  bushels.     64  pecks  +  3  pecks  =^ 

^^P"^-  67  pecks. 

Z_  One  peck  =  8  quarts.    In  67  pecks  there  are 

536  qt.  ^  times   as  many  quarts.     8  times  67  =  536. 

2  There  are  536  quarts  in  67  pecks. 

One  quart  =  2  pints.     In  536  quarts  there 

1073  pt.  are  2  times  as  many  pints.    2  times  536  =  1072. 

1072  pints  +  1  pint  =  1073  pints. 
16  bu.  3  pk.  1  pt.  =  1073  pints. 

1.  Reduce  8  bu.  3  pk.  1  pt.  to  pints. 

2.  Reduce  15  bu.  3  pk.  to  quarts. 

3.  Reduce  12  bu.  1  pk.  3  qt.  to  pints. 

4.  Reduce  3  pk.  6  qt.  to  pints. 


264  COMPOUND  NUMBERS. 

To  reduce  a  compound  denominate  number  to  a  lower 
denomination : 

Multiply  the  highest  denomination  by  the  number  of  ones  of 
the  next  lower  which  make  one  of  the  higher,  and  add  to  the 
product  the  given  number  of  the  same  denomination. 

Proceed  in  like  manner  with  each  successive  result,  until  the 
number  is  reduced  to  the  required  denomination, 

343.  Reduce  689  pints  to  bushels. 

2  )  689  pt.  There  are  in  689  pints  as  many  quarts 

Q  \^iAA    +   _L  1     +  ^^  there  are  times  2  pints,  which  is  344, 

8  )6^  qt.  +  1  pt.         ^^j^Ij  ^  pjj^^  remaining  undivided. 

4  )  ^'^  pk  There  are  in  344  quarts  as  many  pecks 

in K     4- '-l    It         '^^  there  are  times  8  quarts,  which  is  43. 

^   *  There  are  in  43  pecks  as  many  bushels 

as  there  are  times  4  i)ecks,  which  is  10,  with  3  pecks  remaining. 
689  pints  -=  10  bu.  3  pk.  1  pt. 

1.  Reduce  817  pints  to  bushels.     168  quarts  to  bushels. 

2.  Reduce  682  pints  to  bushels.     95  pints  to  pecks. 

3.  Reduce  125  quarts  to  bushels.     87  pints  to  pecks. 

To  reduce  a  compound  denominate  number  to  a  higher 
denomination : 

Divide  the  given  number  by  the  number  of  ones  that  make 
one  of  the  next  higher  denomination. 

Divide  this  quotient  and  each  successive  quotient  in  like 
manner,  until  the  7'equired  denomination  is  reached. 

The  last  quotient,  with  the  several  remainders  annexed  in 
proper  order,  is  the  result  required. 


LIQUID  MEASURE.  265 


LIQUID  MEASURE. 

344.  Liquid  Measure  is  used  in  measuring  liquids.  The 
denominations  are  gills,  "pints,  quarts,  gallons,  and  barrels. 

4    gills  (gi.)  -  1  pint  (pt.). 
2    pints         =  1  quart  (qt.). 
4    quarts       =  1  gallon  (gal.). 
31i  gallons     =  1  barrel  (bbl). 

The  gallon  contains  231  cubic  inches. 

l>j  pints  liquid  me&sure  equal  1  pint  dry  measure. 

The  barrel  contains  31i  gallons ;  the  hogshead  63  gallons. 

1.  Reduce  15  gallons  to  pints.  Reduce  18  gallons  to 
gills. 

2.  Reduce  17  gal.  1  qt.  1  pt.  3  gi.  to  gills.  Reduce  8 
quarts  to  gills. 

3.  How  many  gallons  in  47  quarts?  How  many  gallons 
in  47  pints? 

4.  Reduce  86  gills  to  quarts.     98  gills  to  gallons. 

5.  Reduce  25  gal.  1  pt.  to  gills.  Reduce  19  gallons  to 
pints. 

AVOIRDUPOIS  WEIGHT. 

345.  Avoirdupois  weight  is  used  in  weighing  all  articles 
except  gold,  silver,  and  precious  stones.  The  denomina- 
tions are  ounces,  pounds,  hundredioeights ,  and  tons. 

16  ounces  (oz.)  -1  pound  (lb.). 

100  pounds  -=  1  hundredweight  (cwt.). 

20  hundredweight,  2000  lb.     =  1  ton  (T.). 


266  COMPOUND  NUMBERS. 


60  pounds 

of  wheat           =1  bushel. 

56 

corn  or  rye  =1        " 

32 

oats              =1 

100 

nails              =1  cask  or  keg 

196 

flour              =1  barrel. 

200 

beef  or  pork  =  1  barrel. 

1.  Reduce  3  tons  to  pounds.  Reduce  6  hundredweight 
to  ounces. 

2.  Reduce  7  cwt.  48  lb.  9  oz.  to  ounces.  Reduce  9  tons 
to  ounces. 

3.  Reduce  54145  pounds  to  tons.  Reduce  3684  ounces 
to  pounds. 

4.  Reduce  36425  pounds  to  hundredweights.  Reduce 
32000  ounces  to  tons. 

5.  Reduce  5  T.  12  cwt.  36  lb.  to  pounds. 

EXERCISE. 

346.  1.  How  many  pint  packages  can  a  seedsman  make 
from  4  bu.  2  pk.  and  2  qt.  of  seeds? 

2.  What  will  IJ  barrels  of  vinegar  cost  at  8  cents  a  quart? 

3.  In  one  season  a  market-gardener  sold  12345  boxes  of 
strawberries,  averaging  1  quart  each.  How  many  bushels 
did  he  sell? 

4.  At  7  cents  a  pound,  what  will  2^  barrels  of  pork  cost? 

5.  If  a  horse  eats  1  pk.  6  qt.  of  oats  in  a  day,  how  long 
will  7  bu.  2  pk.  last? 


MEASURES  OF  LENGTH,  267 


MEASURES  OF  LENGTH. 


347.  In  measures  of  lengths  and  distances,  the  denomi- 
nations are  inches^  feet,  yards,  rods,  and  miles, 

12    inches  (in.)  =1  foot  (ft.). 

3    feet  =1  yard  (yd.). 

5i  yards,  or  16J  feet   =1  rod  (rd.). 
320    rods  =1  mile  (mi.). 

1760    yards,  or  5280  feet  =  1  mile. 

1.  Reduce  12  rods  to  feet. 

2.  Reduce  15  rd.  3  yd.  2  ft.  to  feet. 

3.  Reduce  136  rd.  4  yd.  to  inches. 

4.  Reduce  18  miles  to  rods. 

5.  Reduce  4  mi.  130  rd.  to  rods. 

6.  Reduce  5  mi.  20  rd.  to  inches. 

7.  Change  to  lowest  denominations:  2^  miles;  16  rd.  25 
ft.;  34  yd.;  16.8  rd.  32^  yd.  18^  ft. 

8.  Change  to  highest  denominations:  16000  feet;  63360 
inches;  3240  rd.:  7040  yd.;  47520  ft. 

9.  Measure  one  side  of  your  school  lot  and  give  the  length 
in  rods. 

10.  How  many  rods  are  there  in  f  of  a  mile? 

11.  40  rods  is  what  part  of  a  mile? 

12.  If  the  large  wheel  of  a  wagon  is  15  feet  in  circum- 
ference, how  many  times  will  it  turn  in  going  5  mi.  182  rd. 
4  yd.? 

13.  In  a  bundle  of  lath  there  are  100  pieces,  each  4  feet 
long.  If  all  the  pieces  of  the  4  bundles  were  laid  end  to  end, 
what  would  be  the  length  in  rods? 


268  COMPOUND  NUMBERS. 

14.  From  A  to  5  is  17  rods.     One  third  of  that  distance 
is  how  many  feet? 

15.  How  long  will  it  take  George  to  walk  a  half-mile,  if  he 
walks  at  the  rate  of  20  rods  a  minute? 


SQUARE  MEASURE. 

348.  In  measures  of  surfaces,  the  denominations  are 
square  inches,  square  feet,  square  yards,  square  rods,  and 
square  miles. 

144    square  inches  (sq.  in.)  =1  square  foot  (sq.  ft.). 
9    square  feet  =1  square  yard  (sq.  yd.). 

30i  square  yards  =  1  square  rod  (sq.  rd.). 

160    square  rods  =1  acre  (A.). 

640    acres  =1  square  mile  (sq.  mi.), 

or  section  (sec). 

349.  A  surface  has  two  dimensions,  length  and  breadth, 
A  plane  surface  which  has  four  square  corners  is  called  a 

Rectangle. 

A  rectangle  which  has  four  equal  sides  is  called  a  Square. 

The  Area  of  a  surface  is  the  number  of  square  units  it  con- 
tains. 

350.  Suppose  the  top  of  a  table  to  be  4  feet  long  and  2 

feet  wide.  There  are  two  rows  of  4 
square  feet  each;  that  is,  there  are  2 
times  4  square  feet,  or  8  square  feet,  in 
the  surface  of  the  table.  The  width  of 
one  end  shows  how  many  times  4  square 
units  must  be  taken  to  give  the  whole  area. 


SQUARE  MEASURE.  269 

To  find  the  area  of  a  rectangular  surface,  a  certain  num- 
ber of  square  units  are  taken  a  given  number  of  times. 

What  is  the  length  of  one  side  of  a  square  yard? 

Measure  off  in  your  schoolyard  a  square  rod.  What  is  the 
length  of  each  side? 

What  is  the  area  of  a  square  that  is  5^  yards  on  each  side? 

351.  To  find  the  area  of  a  rectangular  surface: 

The  length  and  breadth  being  given  in  the  same  denomino, 
tion,  multiply  the  length  by  the  breadth. 

EXERCISE. 

352.  Reduce: 

1.  140  square  rods  to  square  feet. 

2.  18  acres  to  square  rods. 

3.  12  A.  50  sq.  rd.  8  sq.  yd.  1  sq.  ft.  to  square  feet. 

4.  1  square  mile  to  square  inches. 

5.  112  sq.  rd.  5  sq.  ft.  to  square  feet. 
Reduce  to  higher  denominations: 

6.  1440  square  rods  to  acres ;  4320  square  rods  to  acres. 

7.  23328  square  inches  to  square  yards. 

8.  10890  square  feet  to  square  rods. 

9.  102400  sq.  rd.  to  square  miles. 

10.  5760  A.  to  square  miles. 


EXERCISE. 


353.  1.  How  many  square  inches  of  surface  has  a  pane 
of  glass  3  feet  long  and  2  feet  wide?  (Make  a  drawing  to 
show  the  number  of  rows  of  square  feet;  the  number  of 
rows  of  square  inches.) 


270  COMPOUND  NUMBERS. 

2.  How  many  .square  inches  are  there  in  J  of  a  square 
foot?    In  I  of  a  square  foot?     (Drawing.) 

3.  How  many  square  inches  of  surface  are  there  in  the 
top  of  a  table  which  is  3  feet  long  and  2h  feet  wide? 

4.  Find  the  area  of  a  floor  which  is  12  feet  by  15  feet. 

5.  A  floor  has  a  surface  of  180  square  feet;  if  its  length  is 
15  feet,  what  is  its  width? 

6.  How  many  acres  are  there  in  a  field  18  rods  long  and  9 
rods  wide? 

7.  At  $48  an  acre,  what  will  be  the  cost  of  a  piece  of  land 
160  rods  long  and  118  rods  wide? 


CUBIC  MEASURE. 

354.  Cubic  Measure  is  used  in  measuring  solids.  Its 
denominations  are  cubic  inrhes,  cubic  feet,  cubic  yards,  and 
cords, 

1728  cubic  inches  (cu.  in.)  =1  cubic  foot  (cu.  ft.). 
27  cubic  feet  =1  cubic  yard  (cu.  yd.). 

128  cubic  feet  =1  cord  (cd.). 

In  measuring  wood,  a  pile  8  feet  long,  4  feet  wide,  and  4 
feet  high  is  called  a  cord. 

355.  A  Cube  is  a  solid  bounded  by  six  equal  squares. 

A  Cubic  Foot  is  a  cube  whose  faces  are  each  one  foot 
square.  .  jo 

The  Solid  Contents  of  a  body  is  the  number  of  cubic  \m$& 
it  contains.  :i>- 


CUBIC  MEASURE. 


271 


The  base  of  this  cube  is  divided  into 
square  feet.     There  are  3  rows  of  3 
square  feet  each,  making  in  all  3  times 
3  square  feet,  which  are  9  square  feet. 
If  upon  each  square  foot  we  place 
3  cubic  feet,  we  shall  have  9  times  3 
cubic  feet,  which  are  27  cubic  feet. 
A  solid  which  is  3  feet  long,  3  feet  wide,  and  3  feet  higli 
is  a  Cubic  Yard,  and  contains  27 
cubic  feet. 

How  many  cubic  feet  are  there  in 
\  oi  2i  cubic  yard? 

How  many  cubic  feet  in  i  of  a 
cubic  yard? 
How  many  cubic  feet  in  |  of  a 
9  cu.  ft.  X  3  =  27 en.  ft.  cubic  yard? 

356.  To  find  the  solid  contents  of  a  rectangular  solid: 

The  length,  breadth,  and  height  being  given  in  the  same 
denomination,  their  product  is  the  number  of  cubic  units,  of 
the  same  name  as  the  linear  units. 


357.  How  many  cubic  feet  of 
sand  will  be  required  to  fill  this 
box? 

How  many  cubic  feet  would 
there  be  in  a  layer  of  sand  1  foot 
high  in  this  box? 

How  many  cubic  inches   are 
there  in  one  cubic  foot?    How  many  square  inches  of  sur- 
face has  one  of  the  faces? 


f 

>TfrV 

272  COMPOUND  NUMBERS. 

Build  the  cubic  foot  of  1-inch  cubes. 
How  many  times  must  144  cubic  inches  be  taken  to  make 
one  cubic  foot? 

EXERCISE. 

358.  1.  How  many  cubic  inches  are  there  in  1  cubic 
yard?    In  J  of  a  cubic  yard?    In  |  of  a  cubic  yard? 

2.  Reduce  12  cubic  feet  to  cubic  inches. 

3.  Reduce  87  cubic  yards  to  cubic  feet;  62^  cubic  yards 
to  cubic  feet. 

4.  Reduce  16  cords  to  cubic  feet;  10}  cords  to  cubic  feet. 

5.  Reduce  20736  cubic  inches  to  cubic  feet. 

6.  Reduce  540  cubic  feet  to  cubic  yards. 

7.  Reduce  9  cu.  yd.  7  cu.  ft.  to  cubic  inches. 

8.  Reduce  18  cu.  yd.  12  cu.  ft.  720  cu.  in.  to  cubic  inches. 

9.  Reduce  1152  cubic  feet  to  cords;  6400  cubic  feet  to 
'  cords. 

10.  How  many  cubic  feet  are  there  in  a  rectangular  block 
of  stone  8  feet  long,  5  feet  wide,  and  3  feet  thick?  (Make  a 
drawing  to  show  this.) 

11.  How  many  cubic  feet  are  there  in  a  pile  of  bricks  8 
feet  long,  4  feet  wide,  and  4  feet  high? 

12.  A  tank  6  feet  long,  5  feet  wide,  and  3  feet  deep  con- 
tains how  many  cubic  inches? 

13.  How  many  cubic  feet  of  air  does  a  room  18  feet  long, 
15  feet  wide,  and  10  feet  high  contain? 

14.  In  digging  a  cellar  16  feet  long,  12  feet  wide,  and  8 
feet  deep,  how  many  cubic  feet  of  earth  must  be  removed? 

15.  A  pile  of  wood  16  feet  long,  5  feet  high,  and  4  feet 
wide  contains  how  many  cords? 

16.  At  $.27  a  cubic  yard,  what  will  it  cost  to  dig  a  cellar 
18  feet  long,  14  feet  wide,  and  9  feet  high? 


TIME  MEASURE.  273 

17.  How  many  cubic  feet  are  there  in  a  stick  of  timber  IS 
inches  wide,  8  inches  thick,  and  12  feet  long? 

18.  What  is  the  value  of  a  pile  of  wood  82  feet  long,  4  feet 
wide,  and  5  feet  high,  at  $4.50  a  cord? 

TIME  MEASURE. 

359.  Time  Measure  is  used  in  measuring  time.  The  de- 
nominations are  seconds ^  minutes,  hours,  days,  weeks, 
months,  years,  and  centuries. 

60  seconds  (sec.)  =  1  minute  (min.). 

60  minutes  =  1  hour  (hr.). 

24  hours  =  1  day  (d.). 

7  days  ,       =  1  week  (wk.). 

365  days  =  1  year  (yr.). 

366  days  =  1  leap  year  (1.  yr.). 
100  years  =  1  century  (C). 

February  has  28  days,  except  in  leap  year,  when  it  has  29. 

September,  April,  June,  and  November,  each  have  30  days; 
other  months  of  the  year  (except  February)  each  have  31  days. 

In  business  transactions,  12  months  are  considered  a  year  and 
30  days  a  month. 

360.  Reduce  to  lower  denominations: 

1.  12  hours  to  seconds;  5  days  to  minutes. 

2.  8  d.  12  h.  40  min.  to  seconds. 

3.  How  many  minutes  were  there  in  the  month  of  Feb- 
ruary, 1904  (1.  yr.)? 

Reduce  to  higher  denominations: 

4.  1440  minutes  to  days;  86400  seconds  to  days. 

5.  52560  hours  to  years;  4743856  minutes  to  years. 


274 


COMPOUND  NUMBERS. 


MISCELLANEOUS  PROBLEMS. 


290  ft. 


60  ft. 


18  ft. 


361.  1.  Find  from  the  dia- 
gram the  number  of  square 
yards  of  tihng  used  for  the  fioor 
of  a  corridor. 

Divide  into  two  rectangles  and 
find  the  area  of  each. 

2.  Find  the  number  of  square 
yards  in  the  floor  of  this  room. 

Divide  into  two  rectangles,  one 
of  which  shall  be  2  feet  by  6  feet. 

3.  How  many  square  yards  are 
there  in  the  ceiUng? 

4.  How  many  square  yards  are  there  in  the  w^alls  of 
a  room  20  feet  by  16  feet,  and  9^  feet  high,  if  no  allow- 
ance is  made  for  doors  and  windows? 

The  area  of  the  four  walls  of  a  i»oom  is  equal  to  that  of  a 
rectangle  whose  length  is  equal  to  the  sum  of  the  four  sides,  and 
whose  breadth  is  equal  to  the  height  of  the  room. 

2  X  20  ft.  +  2  X  16  ft.  =  72  ft.      72  ft.  x  9i  ft.  =  684  sq.  ft. 

684  sq.  ft.  -5-  9  =  76  sq.  yd. 

Draw  the  rectangle  which  represents  the  area  of  the  walls  of 
the  room.  30  ft. 


5.  How  many  square  yards  are 
there  in  walls,  floor,  and  ceiling  of 
this  room? 


6.  How  many  square   yards  are   there   in  a  roof,  the 


MISCELLANEOUS  PROBLEMS.  275 

rafters  of  which  are  16  feet  long  and  the  ridge-pole  25  feet 
long? 

7.  If  the  height  of  a  staircase  is  15  feet,  and  that  of 
each  step  is  9  inches,  how  many  steps  are  there  in  the 
staircase? 

8.  How  many  cords  of  wood  are  there  in  a  pile  40  feet 
long,  4  feet  wide,  and  5^  feet  high? 

9.  How  many  cords  of  wood  can  be  piled  under  a  shed 
24  feet  long,  18  feet  wide,  and  12  feet  high? 

10.  How  many  boxes,  4  inches  long,  3  inches  wide,  and 
2  inches  deep,  can  be  packed  in  a  box  3  feet  long,  3  feet 
wide,  and  2  feet  deep,  measured  on  the  inside? 

11.  How  many  fence  boards,  each  16  feet  long,  are  re- 
quired to  fence  a  field  80  rods  long  and  40  rods  wide,  the 
fence  being  4  boards  high? 

12.  Mr.  A^s  orchard  covers  2^  acres.  Allowing  two 
square  rods  for  each  tree,  how  many  trees  are  there? 

13.  How  many  loads  of  earth  of  1  cubic  yard  each  will 
be  needed  to  fill  in  a  lot,  45  feet  front,  90  feet  deep,  to 
raise  it  1^  feet? 

14.  The  factors  of  a  dividend  are  16,  50,  and  9;  of  the 
divisor,  15,  8,  and  2.     What  is  the  quotient  ? 

15.  A  farmer  gave  55  sheep  for  11  young  horses  worth 
$60  each.     What  money  value  did  he  get  for  each  sheep? 

16.  At  60  cents  a  cord,  how  many  days  will  it  take  a 
man  to  earn  $75.00,  if  he  saws  2  cords  of  wood  a  day? 

17.  If  a  turkey  weighing  10^  pounds  costs  $1.68,  what 
is  the  cost,  at  the  same  rate,  of  one  that  weighs  15f 
pounds? 

18.  At  1^  dollars  each,  how  many  lamps  can  be  bought 
for  65  dollars? 


276  COMPOUND  NUMBERS. 

19.  At  iV  of  a  dollar  per  yard,  how  many  yards  of  rib- 
bon can  be  bought  for  2j  dollars? 

20.  A  gentleman  gave  away  I  of  the  books  in  his 
library,  lent  i  of  the  remainder,  and  sold  i  of  what  was 
left.  He  then  had  360  books  remaining  How  many  had 
he  at  first  ? 

21.  If  a  lady  spends  4f  dollars  per  month  for  carfare, 
in  what  time  will  she  spend  $27^? 

22.  The  owner  of  a  schooner  sells  .35 J  of  the  vessel  to 
the  captain.     What  part  does  he  still  own? 

23.  The  minuend  is  67.081.  What  must  the  subtra- 
hend be  to  leave  a  remainder  of  56.009? 

24.  A  owns  t\  of  an  iron  foundry  and  sells  .75  of  his 
share  for  $2100.     What  is  the  value  of  the  whole  foundry? 

25.  A  flour  merchant  bought  137  barrels  of  flour  at 
$7,875  per  barrel.  He  sold  89  barrels  at  $9,378  per  bar- 
rel, and  the  remainder  brought  only  $5.80  per  barrel. 
What  was  his  gain? 

26.  Two  men  start  from  the  same  place  and  travel  in 
opposite  directions.  One  travels  119.33  miles  a  day,  and 
the  other  123.75  miles  a  day.  How  far  will  they  be  apart 
at  the  end  of  six  days? 

27.  Supposing  that  each  child  in  a  schoolroom  ought  to 
have  80  cubic  feet  of  air,  how  many  children  should  sit  in 
a  room  which  is  20  feet  long,  18  feet  wide,  and  12  feet 
high? 

28.  The  walk  from  our  kitchen  door  to  the  stable  is  75 
feet  long  and  4.5  feet  wide.  How  many  bricks  does  it 
contain,  each  brick  being  8  inches  by  4  inches? 

29.  How  many  times  is  4  cubic  inches  contained  in  a 
four-inch  cube? 


YB  35810 


I       ■     ,-  ^,V-;---«.. 


541533 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


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m^m^mm^mmmm^s^rmmm 


^    Mi)t  SCormal  iEmtBt  tit  Nutnlirr   ^ 


Cook  and  Cropsey 

ARITHMETICS 

INDIANA      EDITIONS 


^ 


a 


& 


^ 


''^^T^ 


Prices  as  fixed  by  Law 

New  Elementary  Arithmetic^       35  cents 
New  Advanced  Arithmetic^  45  cents 


AHY  DEVIATION   FROM    THESE   PRICES 
SHOULD  BE   IMMEDIATELY 

REPORTED  TO 

Silver^  Burdett  &  Company 

Fuhiiskers^    Chicago^    Illinois 


^ 


a 


